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."

This may just be it.
The team has created Orion, software which integrates Leap Motion into virtual reality environments.
While the likes of Oculus and HTC's Vive are experimenting with complex, often clunky controllers for VR - Leap Motion's tech allows for an accurate reconstruction of your entire hand.
The software has been released to developers today, and works with existing Leap Motion devices that have already been sold.
Leap Motion chief executive Michael Buckwald told the BBC that it was working with all the major VR makers to embed the device within their headsets.
For now, however, the device rests within a little mount attached to the front of the headgear.
The company hopes the tech will pave the way for innovative new user interfaces, as well as just fun.
After much initial excitement a few years back, Leap Motion has failed to capture the imagination of technology users and sales of the $79 device have been modest.
Could this be the company's killer app?
Follow Dave Lee on Twitter @DaveLeeBBC and on Facebook

A grassroots initiative - entitled Team Personal Best - aims to attract people of all ages, abilities and levels of fitness to take part in athletics-themed activities run by clubs and community groups around the UK.
Clubs can submit events at the Team Personal Best website.
An event can be anything athletics-related: a family sports day or fun run, a sports club open day, coaching course or more, with suggestions listed on the submission page. It's a chance to bring this year's biggest global sporting event to your local area and foster community links in the process.
More than 100 events have been registered and anyone wanting to get involved can use the event finder to discover what's going on in their area.
Participants are encouraged to use social media to share their personal-best times - or any stories of achievement, no matter how big or small - with the hashtag #TeamPersonalBest.
One of the clubs already signed up is So Let's Go Running Bexley, which has registered its summer running events for newcomers.
Claire Osmon, who was a running novice before joining, says: "I came along as a complete beginner and Brian and Dawn [Bexley organisers Brian Page and Dawn Annett] have made me so welcome and put me at ease.
"I'm incredibly unfit but they still praise and encourage me and totally make me feel like I'm part of the group. The whole group is amazing and feels like a big family."
Team Personal Best is part of the London 2017 Inspiration Programme, which comprises 11 projects aimed at harnessing the impact of the championships to boost nationwide participation in the volunteering, community, disability, schools and international sectors.
The IPC World Para Athletics Championships will be held at London Stadium from 14-23 July, followed by the IAAF World Athletics Championships at the same venue from 4-13 August.
You can watch the action from the World Athletics Championships live on BBC TV and Red Button, with coverage of both events on radio and online.
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.
[NEXT_CONCEPT]
Leap Motion's precise movement tracking device has long been criticised for being a great idea in need of a practical application.
[NEXT_CONCEPT]
As London prepares to host both the World Athletics and World Para Athletics Championships this summer, the organisers are encouraging the wider public to get active in support of the events.