Steve Williams, the British ambassador to Bulgaria, was appointed on Tuesday and will take up the post in April.
Both islands agreed to set up a Brussels office last year, to ensure their interests were represented in the European Union.
Mr Williams said he has a lot to learn ahead of taking up his new job.
He said: "I'll be very keen to spend some quality time on the islands to get to know people, to get to know the issues.
"Once the office is up and running properly and I'm established it will be really important to come back regularly."
Guernsey's Chief Minister Lyndon Trott described the role of the office as "vital" in how the Channel Islands "engage with Brussels and the European Union over the coming years".
The appointment of a deputy director to assist Mr Williams in his new role is expected to be announced shortly.

First Greater Manchester plans to increase the price of onboard tickets by 10p in January but freeze the cost of those bought via its mTickets app.
It said it wanted to encourage customers to buy tickets in advance on smartphones to speed up journey times.
Passenger group TravelWatch NorthWest said it may reduce delays but penalised those without the technology.
A spokesman for the bus operator said about 15,000 passengers already use the app and its research showed boarding times would be 75% faster if all passengers used it.
He said the company were confident freezing ticket prices on the app would encourage more customers to pay that way.
TravelWatch NorthWest's John Moorhouse said while he understood it was "an incentive to use the app, a lot don't have the internet and rely on buying [tickets] on the bus".
He also said it was "unfortunate" for the 22% of passengers who do not travel with smart phones.
The majority of single onboard tickets will see a 10p increase from 2 January.
The man chosen to head up the Channel Islands' new Brussels office has admitted he has little first hand knowledge of the islands.
[NEXT_CONCEPT]
Passengers buying tickets onboard some Greater Manchester buses are to pay more than those using a smartphone app.