Monthe follows Conor Wilkinson and Joss Labadie in joining Taylor's side, and he will officially link up with the Saddlers on July 1 after his deal at Prenton Park expires.
The 6ft 4in stopper won three play-off finals - two in the National League, one in League Two - during his time with both Forest Green Rovers and Tranmere.
“I’m very delighted to be here. It’s an exciting project, it’s a big club and I’m very happy," said Monthe.
“The manager wants to bring a new identity to the football club on the pitch and I feel like I will be able to bring that with my qualities and my experience to help this club progress and go up.
“I’m aggressive, I’m neat with my football, I’m a leader and I just want to win.”
Taylor expressed his delight at bringing Monthe to the Banks's, too, as he said: "I’m really happy to bring Manny to the club.
“He’s a player we identified as somebody who would fit into our structure and the way we want to play.
“He’s played a lot of football over the last two years and had exposure to League One with Tranmere.
“He’s hungry for success and his ambition matches ours which is fantastic."
Taylor added: “It’s a real show of intent from the football club that we’re able to secure a player of Manny’s calibre.
“I think the fans will see performances from him and characteristics that resonate with the people of Walsall.”