Mason, 22, pleaded guilty to a charge of sexual assault in January following an incident at a Bawtry bar last year.
He was handed a six-month prison sentence, suspended for two years, and placed on the sex offenders’ register for seven years.
Mason’s contract was cancelled by Rovers in March after he withdrew an appeal against his dismissal.
Despite his background, ex-Rovers chief Ferguson is adamant that Mason – who the Scot brought to the Keepmoat Stadium – deserves a second chance in the game with Posh.
Ferguson said: “This could be viewed as a controversial signing given what happened to him earlier this year,”
“Obviously the boy has made a massive mistake, but I do believe he deserves another chance. He has admitted he has made a mistake. He had poor advice from his legal team, which is something he is aware of, but clearly as a club, we feel we can move on from it.
“There were several other clubs in for his services. We have done well to get the deal over the line. He is a very versatile player, he was excellent for me at Doncaster and there is no question that he has the right character.
“He can play in a number of different positions, (is) technically good with both feet and he was ‘Mr Consistent’ at Doncaster.
“Working with him in the time we did, I am fully aware that what happened involving him is not part of his personality.
“Niall is not the person that people may view him as from the outside based on that one incident.”
Middlesbrough are aiming to have a new manager in place by the end of next week after the club narrowed down their search to three candidates.
Former Boro player and current coach Jonathan Woodgate is the favourite to land his first senior managerial post, while former Watford and Fulham manager Slavisa Jokanovic is believed to have spoken to the club about the vacant role, although his financial demands are thought to be an obstacle.
Ex-Boavista and Braga coach Jorge Simao, who has links to one-time club advisor Peter Kenyon, has also emerged as an alternative candidate.
Tony Pulis left the Teesside club just over three weeks ago.
Barnsley head coach Daniel Stendel has been linked with the position, but the Teessiders have not contacted or approached any club to speak to any manager currently in work.