The midfielder will officially join the Saddlers on July 1st upon the expiry of his contract at Rodney Parade.
The 30-year-old has spent the last five seasons with the Exiles and captained the club for the previous four.
“I’m buzzing to be here,” said Ladabie.
“It’s an amazing club, with an amazing stadium and an amazing manager. I can’t wait to get started.
“The club in itself is a League One club for me and I want to try and play my part in getting us to that level.
“I had a meeting with Matt (Taylor) and it was really productive, really positive and the prospect of playing under him with his ideas and philosophy was very attractive.”
Labadie played 146 times in South Wales, scored 19 goals and helped the club reach two play-finals.
He netted six times in the 2020-21 season, including the winner at the Banks’s Stadium back in February.
He began his career at West Bromwich Albion and enjoyed loan spells at Shrewsbury Town, Cheltenham Town and Tranmere Rovers before moving to the then League One side on a permanent basis in the summer of 2010.
The transfer is subject to EFL, FA and international clearance.