The 23-year-old will compete for the number nine shirt in 2019/20 after an impressive couple of seasons with the cherry-and-whites.
Vellacott has racked up 45 appearances for Gloucester to date, having crossed the whitewash on 12 occasions.
His breakthrough season came in 2017/18 where he made 27 appearances, scoring seven tries and subsequently being called up to train with the England squad.
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He previously spent time at Hartpury College, while he was also a part of the Scotland Under 20 squad for the Junior World Championship in 2015.
Wasps Director of Rugby Dai Young said: “Ben is a young player with a huge amount of potential.
“He is a hungry young athlete who will be keen to compete for a starting place and that’s exactly what we need in order to drive standards across the squad.
“We’re looking forward to having him join in the summer as the pace at which he plays the game is something that will no doubt benefit our backline.”
Vellacott said: “The chance to play for such a historic club as Wasps is something that was too good to turn down.
“Wasps are known for their attacking brand of rugby and I think that’s something that certainly suits my game so hopefully I can play a big part in helping the Club push forward and compete with the very best for trophies and titles in the years to come.
“In the meantime I’ll be giving it everything in a Gloucester Rugby shirt till the end of the season to help us finish on a high.”
Simpson to make Gloucester switch in summer
Wasps scrum half Joe Simpson will be leaving the Club at the end of the season to join Gloucester Rugby.
Simpson, who joined the Wasps Senior Academy in 2006 before featuring for the first-team in 2008/09, has gone on to make 248 appearances in the Black and Gold to date.
The 30-year-old has been part of a Wasps side that has reached the Premiership play-offs in each of the last three seasons, including a final appearance in 2016/17.
Simpson said: “It is with a heavy heart that I leave Wasps. The Club has been a second home for me over the last 15 years.
“It has shaped me as a player and as a person. The players, staff and fans have made this journey so special and I am extremely privileged to have been able to represent this great club and will always be grateful.
“It goes without saying that I will give my all in the Black and Gold till the end of the season and hopefully I can finish on a high note.
“Wasps will always hold a special place in my heart.”
Wasps Director of Rugby Dai Young said: “Having come through the Club’s Academy system, Joe has gone on to be capped by England and the fact that he is soon set to make his 250th appearance for the Club, demonstrates his consistency and also his commitment to the Club during that time.
“When you look at some of the greats for Wasps Rugby, he has to be up there and what’s important for me is that he gets the send-off he deserves over the next few months.
“We’d like to thank him for all his efforts and wish him all the best in his next venture.”
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