Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
Wellens, 33, returned to the club from Leicester City in the summer and has played 24 times this season in the south Yorkshire club's return to the Championship, collecting eight yellow cards.
Chief executive Gavin Baldwin said: "The owners and manager have worked incredibly hard to ensure we manage to keep Richie at the club long term.
"This is great news for everyone involved and a clear signal of the owners intent for the future of Doncaster Rovers."
Wellens, who started his career at Manchester United, played for Blackpool and Oldham Athletic before his first spell with Doncaster began in the summer of 2007.
He left Rovers to join the Foxes for a fee of £1.2 million in 2009 before rejoining Doncaster last summer in a short-term deal after a loan spell with Ipswich Town.