The 23-year old back-rower has spent his whole career with Saints after making his debut at the club in 2012.
The Knights are coached by former St Helens boss Nathan Brown, who made Greenwood a regular part of his team at Langtree Park.
A Saddleworth Rangers product, the forward won the 2014 Super League grand final with Brown at Saints.
The Titans are home to fellow Englishman Dan Sarginson, after he joined from Wigan.
A key stumbling block remains his contract, with Greenwood tied down to St Helens until the end of 2017.