Woodyard - who until recently was captain of League Two side AFC Wimbledon - joins the Minstermen on a two-year deal.
The 30-year-old midfielder was a title winner with Lincoln City in 2016/17 before going on to establish himself in the EFL with the Imps and Peterborough United.
He told the club's official website: "It was a fairly easy decision.
"The club looks like it's really going in the right direction and it will be a great time to get on board.
"I’ve won this league before with Lincoln City and I know what it takes to be successful at this level. I feel my experience can bring a lot to the side."
Woodyard played a part in Lincoln's run to the League Two play-offs, EFL Trophy final and FA Cup quarter final.
He made over 30 appearances in League Two for the Dons last season.