One of League Two’s leading midfielders last season, the 26-year-old was voted into the PFA’s divisional team of the year alongside Bolton’s Eoin Doyle and Ricardo Santos.
He featured in a mammoth 53 games for the Exiles in all competitions, including the narrow play-off final defeat to Morecambe at Wembley.
Sheehan had spent nearly five years with the South Wales club, having initially joined them on loan from Swansea City.
During his four-year tenure at Rodney Parade he made 164 appearances, finding the net on 15 occasions.
News of Wanderers’ interest in Sheehan broke last week, prompting a flood of well-wishes for the player on social media.
“I’m delighted to sign for such a big club with the ambitions they have,” he said.
“That’s one of the reasons why I joined. I want to be part of the journey they are on and get Bolton Wanderers back to where they belong.
“When speaking with the manager he expressed his desire to sign me and told me his ambitions, and that really attracted me to be part of it.
“Also his style of football and the way he wants to play suits me so I feel it’s a good match.
“I can’t wait to play in front of the Bolton Wanderers fans. Even before it was announced I had loads of messages from them! I think this just shows the size of the fan base at this club.”
Ian Evatt was happy to add another strong box-to-box midfielder to his ranks and believes Sheehan has the right character to make a big impact in League One with the Whites.
He said: “Josh is a player I have tracked and known about for a long time and I am delighted to have signed him.
“He’s very good technically and is an intelligent and excellent footballer. He’s a Welsh international who has had a great season with Newport, who he has captained and he was also named in the PFA Team of the Year.
“He will add quality and competition to our very strong midfield area and I’m looking forward to working with him.”