Prop Mayhew, who was born in New Zealand but qualifies for England through his father, has made the switch from North Harbour, while scrum-half Bolt was at Bristol last season.
Mayhew is one of three rugby-playing brothers, with Richard having moved to Newcastle from Esher, while Michael is on the books at Wasps.
Harlequins director of rugby Conor O'Shea told the club's official site: "Nic comes from a family steeped in rugby.
"He is young, explosive and has a huge desire to make an impact in the game. From watching him and talking at length to Craig Dowd, who has coached him, we have no doubt he will flourish in this environment."
Bolt, who previously played for Exeter and Taunton, will provide cover for the No.9 shirt, particularly as Danny Care is likely to be involved with England at the World Cup and RBS Six Nations.
Bolt, who was part of the England junior set-up alongside Care, will face competition from Karl Dickson and academy prospect Sam Stuart for a place in the first team.
Bolt joined fellow new-boys Mayhew and Matt Hopper (Cornish Pirates) at the start of pre-season training at the Stoop, however the club's other summer signing Tim Fairbrother will team up with the squad in the middle of July.
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