Maintenance engineer Ian Ebbs, of Old Station Yard, Morton, was working at the St Ives Web magazine publishing plant in Fengate, Peterborough, when he became trapped on Monday.
Firefighters, paramedics and work colleagues battled to free the 43-year-old from the machine, but he suffered severe internal injuries and died in hospital hours later.
Speaking on behalf of Mr Ebbs's wife, Jackie, and children, Matt, 15, and Zoe, 13, his father-in-law Derek Ball, from Werrington, said: "We are totally distraught. Ian's tragic death has come as a devastating loss to all of us and it will take a very long time for us come to terms with what has happened.
"Ian was the best father, husband, brother, son and son-in-law that anybody could ever wish for. He was always friendly and ever-willing to help anybody in need.
"Until this accident the hopes of Jackie, Matt and Zoe were for a very bright future full of happiness, but this accident has robbed them of that future.
"Our distress is made worse by the thought that Ian will never again have the opportunity to play with his children, share their experiences at school, lead his daughter down the aisle when she eventually marries or know the pleasure of having grandchildren.
"All Ian did was go to work to earn money for his family and now he is not coming home. A tragedy like this should never have to happen to anyone.
"He will be greatly missed not only by his family, but by so many other people whose lives he came into contact with."
Mr Ebbs was involved in the accident during a night shift at the St Ives plant in Storey's Bar Road, Peterborough.
He became trapped in the printing press as he maintained the machine at about 10.45pm on Monday and remained trapped for several minutes before he was released.
The Health and Safety Executive has launched an investigation into the tragedy.

Pay your tribute to Ian Ebbs on this website by emailing smeditor@stamfordmercury.co.uk

A spokesman for St Ives Web confirmed an investigation was underway at the plant.
He said: "The incident is subject to investigation and, as such, St Ives is unable to make further comment until the appropriate authorities have completed the investigations."
The site is now back in production, but the press that was involved in the accident has been cordoned off as the investigation continues.
St Ives chief executive Brian Edwards said: "Our thoughts are with the engineer's family and friends at what must be an extremely difficult time.
"Our efforts are focused on supporting the family, friends and colleagues of our member of staff."
A special assembly has this week been held for youngsters at Bourne Grammar School, where Mr Ebbs' children are both pupils.