In exchange for Welker, the Patriots sent their 2007 second- and seventh-round draft picks to Miami.
After the trade, Welker agreed Tuesday to a five-year, $18.1 million contract includes a $9 million signing bonus, ESPN.com's John Clayton reported.
ESPN.com first reported Saturday that the Patriots planned to sign Welker to a restricted free agent offer sheet. But the two teams obviously decided to avoid the red-tape and uncertainty that accompanies such a transaction and opted for a trade instead.
The Dolphins last week made Welker a qualifying offer of $1.3 million.
Had the Patriots officially executed the offer sheet to Welker, the Dolphins would have had seven days to either match it or pass on it. Under that scenario, if Miami matched the offer sheet, it would have retained Welker at the terms of the deal New England negotiated with him. If the Dolphins did not match the offer sheet, they would have received a second-round pick in the 2007 draft from the Patriots as compensation.
The trade agreement, though, renders moot the question of whether Miami would have matched an offer sheet and allows Welker to immediately move to the Pats. Welker should quickly upgrade a position where the Patriots have struggled of late to develop young players.
Welker, 25, is a terrific, if unheralded playmaker who has earned a spot on the ESPN.com "all unsung" team each of the past two seasons. Used principally as a return specialist in his first two seasons in the league, Welker emerged as a viable receiving threat in 2006, with 67 catches for 687 yards and a touchdown.
The former Texas Tech standout originally entered the NFL with San Diego in 2004 as an undrafted college free agent. He was waived by the Chargers early in the 2004 season and signed with the Dolphins shortly thereafter.
In 47 appearances, including three starts, Welker has 96 receptions for 1,121 yards and one touchdown. He has returned 170 kickoffs for an average of 22.7 yards and one touchdown and has 127 punt returns for a 9.7-yard average and one score.
On another front, a source close to Bill Belichick reacted with skepticism Monday to reports that the New England coach is "enamored of" Randy Moss and might consider acquiring the Oakland Raiders wide receiver in a trade.
Said the source: "I'd be very cautious about how I treat second- or third-hand information about what's going on in the mind of Belichick when it comes to this stuff. Unless you're hearing it directly [from Belichick], you're taking a big leap. It happens every year with the Patriots, about free agency and draft plans, a lot of agendas and speculation that rarely end up happening."
Senior writer Len Pasquarelli covers the NFL for ESPN.com.