A cloud of speculation has followed the Origin fullback all season, but News Limited reports that he has signed a $1 million-plus contract with the Chooks.
Earlier on Thursday, the Tigers gave Tedesco and Woods a 24-hour deadline to decide on their futures.
News Limited reports the deals for both players had already been finalised when Wests gave the deadline, but that the club didn't know about them.
The brightest prospect of the so-called 'Big Four,' Tedesco will be the biggest loss for the Tigers.
Despite re-signing winger David Nofoaluma and half Luke Brooks, Tedesco joins Woods and Mitchell Moses out the door.