The 18-year-old scored 13 goals in 11 appearance for the under-18s last season and netted seven times in 15 outings for the under-23s.
That form led to speculation suggesting Cleary could leave The Hawthorns.
Premier League sides Arsenal, Everton and Newcastle have all been linked with moves for the forward who has progressed through Albion’s academy.
German giants Bayern Munich and Bayer Leverkusen have also reportedly sent scouts to watch him.
It is understood Albion offered Cleary what they felt was an attractive package to keep him at The Hawthorns.
But the striker decided to move on – with Cleary believed to have told the club his decision in March.
His decision to leave is understood to be the reason why the teenager hasn’t featured for Albion’s under-23s recently.
It also means Cleary won’t play when the Baggies take on Wolves in the Premier League Cup final on Friday.
As well as Cleary, fellow striker Owen Windsor has also confirmed he is leaving Albion this summer.