The 35-year-old has inked a two-year deal at the Riverside after agreeing personal terms and passing a medical.
Coyne will help fill the void left by Ross Turnbull's departure to Chelsea and Boro boss Gareth Southgate was delighted to land the experienced custodian.
"Danny is an excellent goalkeeper who will push for a first team place this season," Southgate told the club's official website.
"He has played at the highest level with Wales and has great experience. Just as importantly, he is the right type of character in that he is very professional, trains well and has a real hunger to claim the number one spot.
"He played 40 games for Tranmere last season, kept 20 clean sheets and was probably the best goalkeeper in League One.
"We feel we need an experienced goalkeeper to challenge Brad [Jones] and Jason [Steele]. Danny has a wealth of experience and would no doubt have played many more times but for injury."
Coyne is looking forward to the challenge of helping Middlesbrough try and win promotion back to the Premier League at the first time of asking.
"Gareth has told he wants us to win the Championship and get the club back in the Premier League where we belong.
"I've played most of my career in this division so I know it very well and I think we've got every chance of going up.
"I feel as fit as I've ever been so I'm coming here to push Brad for a first team place and do all I can to contribute towards us winning promotion."