An England U20s graduate, Bassett topped the RFU Championship try-scoring charts last season with 14, and he has been in excellent form again this season, scoring eleven league tries to date for Bedford and also representing the RFU Championship XV against the New Zealand Maori in Doncaster in November.
Bassett will link up with Tommy Bell, Nathan Morris and Alec Hepburn at London Wasps who were all teammates when he represented England at the Junior World Championships in South Africa last summer.
London Wasps Director of Rugby Dai Young said: “Josh fits the bill perfectly for what we are trying to achieve here. He’s young, he’s very ambitious and he’s English and he’ll be an excellent addition to our set up. We have some very talented wingers in our squad but he’s got a big future and having impressed hugely at Championship level we’re looking forward to seeing what he can do with us.”