New teammate Scott Chandler, meanwhile, is looking forward to playing for his former AFC East rival.
The two free-agent signees recently agreed to two-year contracts with the Patriots.
Sheard, a defensive end/linebacker hybrid with Cleveland, had the Patriots on his radar coming out of college at Pittsburgh in 2011.
''I visited there coming out my rookie year,'' he said. ''I thought I was going to be drafted coming out as a rookie. I got a second shot at it.''
Sheard played four years with the Browns, recording 23 career sacks. But his playing time diminished over the last two seasons and he started only five games in 2014.
In New England, he will be part of what the coaches hope will be a stronger front seven after the loss of cornerbacks Darrelle Revis and Brandon Browner from the Super Bowl-winning defense. He adds depth at the hybrid spot that already includes Chandler Jones and Rob Ninkovich.
''Meeting with the coaches again, same coaches, coming from a program where I was changing coaches every year, there's some consistency there,'' Sheard said. ''Just the fact that guys have been doing it for a while and they want to win, I want to be a part of that.''
Chandler, who has 1,700 yards receiving over the last three seasons for Buffalo, caught six passes for 105 yards in the Bills' 37-22 loss to New England last October.
His decision came down to picking between New England and Baltimore, calling the teams ''two really good organizations.''�
''I've been playing for a while and I wanted to be part of the organization that has a pretty good chance to win,'' he said, adding that coach Bill Belichick and owner Robert Kraft have done an ''amazing'' job of creating and sustaining success.
''I'm looking forward to going into this year and doing whatever I can to be a part of that,'' Chandler said.
Sheard, who called his NFL career ''shaky'' and ''up and down,'' feels the same way after picking the Pats over what he said were coaching connections with Tampa Bay and Seattle.
''Just coming in and hearing from the coaches, about all the great things going on, coming from a not-so-good program to a great program that they're winning and doing well, I'm just excited,''� he said. ''I want to win in the league and I want to be a part of a great organization. That was a big part of me signing.''
Sheard recalled his pre-draft visit to Foxborough four years ago.
''It was real businesslike, real focused,'' he said. ''You could tell it's going to be all business once we get there. It was a bit nerve-wracking, I can't lie to you. I was a bit nervous.''
''I'm more focused and more hungry,'' he said, ''than I've ever been.''
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