Their contracts had been due to expire in the summer.
Butcher told BBC Scotland: "The club needed some stability and we needed that as well and we can now build on what we are trying to do here."
The former Coventry, Sunderland, Motherwell and Brentford manager took charge of Caley Thistle in January last year, with former Well and Swindon boss Malpas joining him as first-team coach.
With their future guaranteed, they can now focus on persuading players to sign new contracts
Inverness chairman George Fraser
They were unable to prevent the side being relegated from the Scottish Premier League and they presently sit third in Division One, nine points behind leaders Dundee but with a game in hand.
"We have had great backing from the board and the fans and the players," said Butcher.
"The circumstances have been very difficult for us since we came in.
"To get relegated was not what we intended and we were so close for that not to happen and this year has been a difficult one.
"We have had to revamp the squad. It's virtually a new team and way of playing and we're still in the mix to go up."
Butcher said his own contract would allow him to plan for next season, with only three players remaining under contract for next term.
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Inverness chairman George Fraser told his club website: "We feel the timing is right rather than leaving the clock to run down on their contracts before making decisions.
"With their future guaranteed, they can now focus on persuading players to sign new contracts and on further strengthening the squad for next season.
"We are still in the promotion race and Terry and Maurice have emerged with considerable credit this season in rebuilding the side after the financial disaster of relegation from the SPL and players departing."
Source: BBC Sport
Source: BBC Sport