Ring completed a move to the Major League Soccer side from 2. Bundesliga side Kaiserslautern on Tuesday.
"At 25, Alexander is a player entering his peak years who has played at a high level over a number of seasons," Vieira said. "He's a midfielder who can contribute on both sides of the game, both defensively and offensively and he gives us another great option either at the base of midfield or box-to-box.
"Alexander has a good engine and is a competitive player which should suit Major League Soccer."
The club used targeted allocation money to acquire the Ring, who said he was eager to contribute.
"As soon as I heard of the interest I was intrigued because I know how big the club is and how well-supported the team is," he said. "It took a long time to get it done but as soon as I knew about the New York option it was clear for me that I wanted to do it. I had to fight for it hard but I'm so happy."
Ring has spent parts of the last four seasons with the Red Devils, making 83 league and cup appearances, scoring eight goals.
Injuries have limited his availability to just 11 league and cup appearances this season. He has also spent time with Bundesliga side Borussia Monchengladbach as well as Finnish clubs HJK Helsinki, Tampere United, and Klubi-04.
Ring has been capped 42 times for Finland, scoring once against Luxembourg in March 2013.
"I've been watching the MLS games they show in Germany on Eurosport and I've learned it's a very physical league and maybe an underestimated one," he said.
"I want to leave my mark -- I think when the people get to know me they will see I'm a winner and always give 110 percent and fight to win."
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