The 23-year-old, born in Truro, made his league debut for Pirates at the age of 19 and has represented Cornwall, Cornwall U20 and England Conference U18.
Hooker Hayes, who moved to Warriors from Bristol Rugby in 2011, has also pledged his future by putting pen to paper on a new contract.
The 22-year-old has made a total of 14 appearances for Worcester, including four in the Aviva Premiership this season. He also scored a memorable first try for the club as Warriors secured a try bonus point against Northampton Saints at Franklins Gardens in September.
Head Coach Richard Hill was delighted to continue his squad build for next season by agreeing deals with the young front row pair.
"Paul Andrew is a player we've been aware of for some time," said Hill. "We keep a track on the best players in each position and have seen Paul's progress in the RFU Championship.
"He is similar to George Porter in that he has massive potential and will only get better. Paul is another excellent product of Cornish Pirates, where he has been well coached and developed, and his attitude is excellent. He will add depth to our first team squad and we are excited that he will join us.
"In the front row you have got to do your apprenticeship and next year is undoubtedly a big season for Ollie," added Hill.
"We feel he can make the step up to play first team rugby in the Aviva Premiership and that's why we've re-signed him.
"He is a very dedicated individual and a very good all-round player who can carry and has excellent hands.
"Now is the time for him to make the step up. This is not a decision we have taken lightly, but Ollie really is the modern day hooker and we have put our faith in him."