Jacob Tamme found the bigger offensive role he was looking for in Atlanta, where the Falcons were seeking a veteran tight end a year after the retirement of Tony Gonzalez.

Tamme agreed to a two-year deal with the Falcons, becoming the sixth free agent to bolt Denver this offseason.

“I loved being in Denver, loved my teammates,” Tamme said in text message while flying to Hawaii on a family vacation Thursday. “It’s not easy to leave a place like that. But the opportunity that presents itself in Atlanta is exciting for me, the chance to go in with a new head coach and build something.”

The tight ends play an integral role in offensive coordinator Kyle Shanahan’s scheme, and Atlanta’s top tight end last year was second-year pro Levine Toilolo, who had 31 catches for 238 yards and two touchdowns in 2014.

Tamme has spent all seven of his NFL seasons with Peyton Manning, although Manning missed their last season together in Indianapolis in 2011 because of injury.

“Obviously they have a very good quarterback in Matt Ryan, who I’m really looking forward to getting to know,” Tamme said. “I’m leaving a good one, too. Ha-ha. That part is tough because Peyton has become a truly great friend of mine and I have been so blessed to be around him and learn from him.

“But this is an exciting opportunity in every way.”

Tamme had 86 receptions and 14 special teams tackles in his three seasons in Denver, including 14 catches for 109 yards and two touchdowns last season. He set career highs with 67 catches for 631 yards and four touchdowns with the Colts in 2010.

His best year in Denver was in 2012, when he caught 52 passes for 555 yards and two TDs, but his role was greatly reduced after slot receiver Wes Welker’s arrival and the emergence of Julius Thomas in 2013, and he was used mainly on special teams.

The Broncos made an offer to keep Tamme while he was visiting with the Falcons on Wednesday.

Although Thomas signed with the Jacksonville Jaguars last week, Tamme still would have settled in as the Broncos’ third tight end this season behind free agent acquisition Owen Daniels and blocking tight end Virgil Green.

Tamme has 178 catches and 10 touchdowns in seven seasons with the Colts and Broncos. He was a fourth-round pick by Indianapolis in 2008 and spent four seasons with the Colts before following Manning to Denver in 2012.