Unrestricted free agents can officially sign with other teams on March 12.
Welker, 31, received the Patriots’ franchise tag last offseason but New England didn’t issue a franchise tender to any player for the 2013 season before Monday’s deadline.
It was first time since 2008 that the Patriots opted not to use the tag.
If the Patriots had used the tag on Welker again this offseason, he would be entitled to a 20 percent raise from his 2012 salary of $9.5 million (paying him $11.4 million in 2013).
Welker finished last season with a team-high 118 catches and 1,354 yards to go with six touchdowns.
He had a team-high eight catches for 117 yards in New Englands 28-13 AFC Championship Game loss to the Baltimore Ravens on Sunday, but he also had a drop on a key third down in the second half.
Welker became the first player in NFL history with five 110-catch seasons and has averaged 112 receptions during his six seasons as a Patriot.