Who must approve a globally distributed satellite to ground laser communication system? Laser Light Communications (US) plan for several dozen optical high speed data links between satellites and ground is described in Aviation Week's article Big Gains On Horizon For Laser Communications Suppliers and Lightwave's online website: Laser Light to leverage free-space optics in space for Optical Satellite as a Service.


  All Optical Hybrid Global Network (or HALO, as laser Light calls it)


The plan is to use lasers to establish optical links between satellites in Earth orbit (MEO) and between them and a network of ground stations. 


  According to the company's website, Laser Light will leverage 8 to 12 satellites in medium Earth orbit to create a network that will offer an initial service capacity of 7.2 Tbps. The satellites will pass signals among themselves and to the ground via free-space optics. The space interconnections will include 48 links of 200 Gbps apiece, as well as 72 steerable up/down links to Earth at 100 Gbps. (my emphasis)


edit: Confirming that the plan is to establish several dozen laser communications link between ground stations and satellites, from the article The Speed of Light: Laser Light and Optus Explain Optical Communications Partnership:


  Laser Light’s hybrid network is broken into two elements: an OSS part and the Ground Network System (GNS). The OSS half is comprised of a constellation of eight to 12 Medium Earth Orbit (MEO) satellites, which beam down data to a GNS via a completely optical spectrum. The data then connects to terrestrial fiber infrastructure, such as the one Optus already has in place. (my emphasis)




above: Graphic from The Speed of Light: Laser Light and Optus Explain Optical Communications Partnership to Via Satellite Magazine Note: since the satellites are in medium Earth orbit (MEO) and not Geosynchronous orbit (GEO), these beams would not be fixed, but in fact scan repeatedly through tens of kilometers of airspace each.

These would not be narrow, millimeter-diameter beams like we see from laser pointers. In order to combat diffraction, they would actually be expanded to at least tens of centimeters in diameter or larger. There is also a chance they would be just outside the visible wavelength range in the (very near) infrared. So I would guess there is a good chance that - depending on the actual implementation - these beams might not actually pose any risk to a pilot if an aircraft passes though one, but I don't know that for a fact.

I would like to know who must approve globally distributed continuous laser data links between Earth stations and orbiting Satellites in the context of aviation safety. 

The answers to the related question How does aviation deal with satellite and Moon laser ranging, and other scientific lasers in the sky? seem to suggest that there are some rules and best practices associated with ground-based lasers from observatories that are used intermittently, but in the case of bidirectional, near continuous laser traffic from dozens to perhaps hundreds of sites (each satellite has 72 independently steerable beams) the existing procedures (having two human spotters watching for planes) would not really be feasible. 

There is some discussion here but I don't see any mention of aviation.
(I've taken a wild stab at an answer, despite my not being a lawyer or legal expert of any kind, since nobody has written an answer in nearly four years.  If you don't like my answer, please feel free to write a better one.  I apologize in advance if I've abuse any legal terms.  It's quite possible that I have come to an erroneous conclusion.)
Your question seems to presume that there is some multinational body, or multinational rules, governing laser beams in the atmosphere.  However, there is no multinational agreement to regulate laser beams in the atmosphere.
Countries are sovereign, with no higher legal authority, and are not required to make any rules, laws, or enforcement bodies without voluntarily agreeing to do so.  Often countries realize that uniform standards or regulations are in their best interests, and make treaties or agreements with other countries to create laws and rules and enforce them.  Sometimes countries voluntarily abide by existing treaties or agreements without actually signing onto the agreement.  In the absence of such formal treaties or agreements between countries, individual countries are free to write, or to not write, whatever rules and laws they like.
One of the functions of the United Nations is to create a list of international treaties and agreements.  The list, known as the United Nations Treaty Series Cumulative Index, can be found here.  The most recent list as of this writing, current to 20 March 2013, sorted alphabetically, is here.  A quick search of the index for the term &quot;laser&quot; reveals only an &quot;Exchange of notes constituting an agreement between the United States and Japan concerning a program for the cooperative research of Eyesafe Laser Radar.&quot;
In other words, there is no multinational agreement to create rules or laws regarding laser beams in the atmosphere, other than those that pertain to aviation safety.  Existing aviation safety legislation seems to agree that pointing powerful lasers at aircraft is something that should be regulated.  However, it seems likely to me that aviation safety treaties are silent regarding laser beams through the atmosphere that are not pointed at aircraft.
To sum up, it has been left to individual countries to write whatever laws they like regarding laser beams in the atmosphere not aimed at aircraft.  Currently it seems likely that few countries have written any such laws.  So companies can currently feel free to plan communications networks using laser beams between ground stations and satellites, since there are few or no laws to stop them, as long as they take care to not accidentally aim laser beams at aircraft.