Jackson is powerful ball carrier who has made a huge impact at London Welsh, having previously represented Bath and Doncaster. His leadership skills were also recognised at international level where he captained England U18s and U16s and was part of the side that won the Four Nations in 2006.
London Wasps Director of Rugby Dai Young said: "Ed is a player I am excited about. He was excellent last season and he's backed it up this year again in the Premiership. He's an explosive runner with great hands and he can play eight and six which will be very useful for us."
London Welsh have also confirmed the transfer.
Jackson, 24, joined the Exiles in 2011 from Doncaster Knights and was instrumental in the club's Championship-winning season, scoring 11 tries in 29 league appearances.
This season, his late try helped the club record its first-ever Aviva Premiership victory - a 25-24 win over Exeter Chiefs at the Kassam Stadium in September. That was one of three tries he scored in 13 Premiership appearances.
In total, Jackson has made 52 appearances for London Welsh in all competitions, scoring 14 tries.
"London Welsh is a club I have huge passion for, perhaps more so than any club I've played for in the past, so I'm sad to move on," said Jackson.
"I've learnt so much under Lyn Jones, he's brought my game on immensely, and there's a great bunch of lads there.
"Leaving London Welsh was a very difficult decision, but ultimately the chance to join Wasps was too good an opportunity to turn down."