The 24-year-old was one of three Pakistan players jailed in November 2011 for conspiring to bowl deliberate no-balls against England in 2010.
He was banned for five years, but returned in January last year.
"He made a mistake and he paid a price for that mistake and as far as we're concerned that's over," Bowden said.
"It is as straightforward as that, there've been one or two other cases with players that have had a history and we've taken the same view.
"It was a relatively straightforward, not an easy choice and one has to think about it, but he paid a price and therefore he should be free to go on and further his career and enjoy his life."
When he arrives next June, Amir will bolster a bowling line-up that has seen Graham Napier and David Masters retire after helping Essex win the County Championship Division Two title this year.
"He's going to bring pace, he's going to bring experience and I hope he brings some ambition," Bowden added.
"Our ambition is to do well in Division One, to stay in Division One, and to do well in white-ball cricket.
"He's going to have a big impact in the second half of the season in four-day, and for the entire Twenty20 competition."
Essex chief executive Derek Bowden says Mohammad Amir must be allowed to get on with his career, with the Pakistan bowler set to join the club in 2017.