Unrestricted free agents can officially sign with other teams starting Tuesday.
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 this past Monday's deadline.
It was the 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, along with six touchdowns.
He had a team-high eight catches for 117 yards in New England's 28-13 AFC Championship Game loss to the Baltimore Ravens, 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 with the Patriots.
Information from ESPNBoston.com's Mike Reiss and Field Yates was used in this report.