Lascelles, who entered the final six months of his current deal with the Magpies at the turn of the year, has been allowed to leave in order to play regular first-team football in the remainder of the season.
The 32-year-old, who is still Newcastle's official club captain, has spent more than a decade with the club after signing in the summer of 2014.
He spent the following season back on loan with Nottingham Forest, but has gone on to make 253 senior appearances for Newcastle, the most recent of which came as a substitute in September's league defeat to Arsenal.
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The last couple of seasons have seen him battling against a succession of injury issues, but prior to that he was a key member of the first-team squad under a number of different managers.
He was a pivotal part of the promotion-winning side under Rafael Benitez, and continued to play a major role in the Premier League under both Steve Bruce and Eddie Howe.
He joins a Leicester side struggling in the bottom half of the Championship, and potentially facing a points penalty before the end of the season that could plunge them into a relegation battle.
Lascelles' departure is likely to be Newcastle's only piece of significant business ahead of today's 7pm deadline, with Howe having conceded on Saturday evening that he does not expect to be making any signings.