The 24-year-old English back row signs for the Club having hugely impressed in the Aviva Premiership this season, after a successful rise through the RFU Championship a year ago.
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.”