A new academy is also being set up at HMP Leeds to equip inmates with construction skills ahead of their release.
Ex-offenders are a potential pool of talent as the industry struggles with an intensifying skills shortage.
Amey is a backer of the education and employment strategy run by the Ministry of Justice.
Andy Milner, CEO of Amey, said: “At Amey, we believe in hiring the best people for the job, no matter what their background or history.
“For us, hiring ex-offenders is not only the right thing to do but it also makes good business sense.
“There is a growing skills gap within our industry and within our prison population there is a pool of highly motivated people learning new skills such as engineering, carpentry and plumbing who just need someone to believe in them to help change their lives.
“The ‘Passport into Employment’ programme we have in place as part of our prisons maintenance contract together with our waste recycling partnership with Recycling Lives is helping to support men and women to transform their lives and demonstrates our commitment to rehabilitating ex-offenders.”