Newhouse was an unrestricted free agent after spending four seasons in Green Bay. He played in 14 games last season, starting two of them.
He was the left tackle at Texas Christian for three years while Dalton was the quarterback.
Cincinnati needed an offensive tackle after losing Anthony Collins as a free agent to Tampa Bay. Newhouse has played both left and right tackle, starting 31 games over four seasons in Green Bay.
McElroy, who spent his first two seasons with the New York Jets after being a seventh-round pick out of Alabama in 2011, announced his retirement from football later in the day. The 25-year-old quarterback started one game in his career, and was sacked 11 times in the Jets' 27-17 loss to San Diego in 2012. He finished his NFL career with 214 yards passing with one touchdown and one interception.
''The future is bright,'' McElroy wrote in a message posted on Twitter in which he thanked the Bengals, Jets and their fans. ''And, exciting things are on the horizon.''
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