Scotland international lock Grimes departs following more than six years on Tyneside, with the duo accompanying players like Owen Finegan and Dave Walder through the exit door.
Fly-half Walder has been strongly linked with a move to Celtic League side Newport Gwent Dragons, while Finegan has attracted interest from other Premiership clubs.
Australian full-back Matt Burke, who recently signed a new two-year contract, will replace Charvis as skipper.
"Matt takes over from Colin Charvis, who led the side last season, but along with Stuart Grimes will not be with us for the coming campaign," said Falcons rugby director Rob Andrew.
"We thank Colin and Stuart for their time with us, and wish them both well for the future."
Burke assumes leadership duties after scoring 21 tries in his 48 starts for the club, and said: "We saw our potential last season with some fantastic performances, beating all four of the top sides in the Premiership.
"The key now is to maintain that form over the course of the whole campaign, and to do ourselves justice with the great talent we have in the squad."
Newcastle have confirmed new arrivals in Northampton wing John Rudd, North Harbour flanker Brent Wilson, Rotherham prop Jon Golding and Otley lock Jason Oakes, with 10 of their academy players promoted to the senior squad.
"The end of last season saw glimpses of what we are capable of when we have the likes of Jonny Wilkinson, Mathew Tait, Jamie Noon and Matt Burke in the same back-line behind our good young forwards, and this is a squad which will develop together over a number of years," added Andrew.
"We have confidence in this squad, and will be allowing them to grow together to fulfil their undoubted promise."