Spratt, 25, joins on a one-year deal, and Samson, 23, on a two-year-deal.
Wales international Spratt said: "I'm excited to be joining London Irish. They play an exciting brand of rugby that appeals to me."
Samson, who has played for Scotland at U20 level, said: "I've enjoyed my time at Edinburgh but a chance to play in the Premiership was not to be missed."
The duo will join the Exiles squad this summer for pre-season training.
Jonathan is a strong, powerful runner, with great feet and good distribution skills.
Spratt made his Wales debut in 2009 in a Test against Canada.
The centre also played for Taranaki in New Zealand's domestic rugby tournament, the Air New Zealand Cup in 2008.
He has not played for Ospreys this season, having damaged his anterior cruciate ligament in pre-season, on his return from an earlier injury.
Samson is a product of Newcastle Falcons' academy and has represented Scotland at all age-group levels.
The Edinburgh-born scrum-half featured in the IRB Junior World Championship in 2008 and this season's IRB sevens circuit tournament.
Ross has a strong pass on him, an eye for the gap and he reads the game well.
London Irish head coach Toby Booth said: "Jonathan is a highly talented young player and another very useful addition to our squad.
"He is a strong, powerful runner, with great feet and good distribution skills.
"Ross is an exciting young talent in Scottish rugby. He has a strong pass on him, an eye for the gap and he reads the game well."

16 April 2016 Last updated at 08:16 BST
Gusts of more than 75 miles per hour were recorded and it became very hard for people to see what was going around them.
Watch the video to see the sandstorm sweep over the province.

TV network NBC announced Sir Elton will host and perform on stage with fellow musical guest and collaborator Leon Russell on 2 April.
It is the singer's first return to the show in nearly three decades.
Meanwhile, Dame Helen will make her debut as host a week later with musical guests Foo Fighters.
Sir Elton last appeared on Saturday Night Live in 1982 when he performed Empty Garden and Chain in a show hosted by Johnny Cash.
He recorded his latest album, The Union, with American musician Russell.
Dame Helen will be soon be seen on screens opposite Russell Brand in the remake of Dudley Moore film, Arthur.
Brand also hosted the show for the first time last month.
Saturday Night live is one of the longest-running programmes in the US with nearly 700 episodes broadcast over 36 series.
London Irish have signed Ospreys centre Jonathan Spratt and Edinburgh Rugby scrum-half Ross Samson.
[NEXT_CONCEPT]
A huge sandstorm hit China's Gansu Province on Friday afternoon, filling the skies with dust.
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Sir Elton John and Dame Helen Mirren have been lined up to host episodes of US comedy sketch show Saturday Night Live in April.