The players join fellow Scotland caps David Denton, Ross Ford, Matt Scott, Alasdair Dickinson, Grant Gilchrist and Greig Tonks in signing up for next season.
"Attracting and retaining quality Scottish players is absolutely critical for us, and is central to our vision, so it's fantastic news for the club that these three have re-signed," said Alan Solomons, the club head coach.
Utility back Cuthbert, who has played 23 times since a summer move from Bath, said: "I think the club is going in a good direction and it's great to be part of a team that's so young and so eager to keep improving. We've got a really good group here and I think we're building something special.
"It's just going to take a bit more grit, with some tough months to come as we look to take the club in a positive direction."
Winger Fife made his Scotland debut against Wales last month after a run of five tries in seven matches for Edinburgh, before a hand injury ended his season, while Brown has now made over 50 appearances for the club since debuting in 2010.