Green, 29, has been a Pro Bowl selection in each of his seven years in the league.
Price was selected 21st overall and is expected to start Week 1 for Cincinnati.
German-born Moritz Bohringer was signed by the Cincinnati Bengals in the NFL.
Boehringer, who stunned observers with his performance at a scouting camp in 2016, hasn't been able to make an NFL team's roster.
After a dramatic night dominated by quarterbacks and trades in Dallas, we recap the first round of the 2018 NFL Draft in full.
Six quarterbacks land in a first round with two huge top-10 trades in our 2018 NFL Draft mock.
With three quarterbacks set to go in the top three for the first time since 1999, we look back at how the careers of that trio panned out.
There are plenty of interesting storylines this upcoming NFL season but here are 10 games you need to watch.
The Saints and Vikings will face off again after last year's divisional round game ended in absolute chaos.
The controversial Bengals linebacker is no stranger to suspensions, having served three during his NFL career.