The highly-rated 19-year-old has impressed during eight first-team appearances and has excelled for the Cavaliers.
He trained with the full England squad ahead of their tour to South Africa over the summer and has represented his country at Under 18 and Under 20 levels.
Lawrence said: “I have really enjoyed my time at Warriors and feel I have been able to learn and develop as a player under the guidance of the coaches over the last five years.
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“I am grateful to the other centres at the Club, especially Millsy, Wynand, Francois Venter and Ashley Beck, who have all helped me get to a stage where I can push for a place in our Premiership squad.
“We have moved forward on the pitch this season and I’m looking forward to being part of this Club’s future.”
Warriors Director of Rugby Alan Solomons said: “Ollie is a very talented young player, who has made tremendous progress this year with some outstanding performances, especially during the European Challenge Cup match against Stade Francais in Paris.
“He is benefitting from playing with international-class centres and it is only a matter of time before he pulls on the England jersey.”
Lawrence, who hails from Birmingham, has been part of the Warriors Academy since the age of 14 and burst onto the first-team scene with a try on his debut against Sale Sharks in November 2017.
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