Leicester-born Cockerill-Mollett is a product of the club's youth Academy and has risen through the ranks at Banks's Stadium to sign professional terms in 2016.
Callum, who has made appearances for the Republic of Ireland's Under-19s, made his senior debut in a 5-2 Checkatrade Trophy victory over Grimsby later Town in August 2016 and has gone on to feature for the development side on several occasions.
Telford boss Gavin Cowan spoke to the press earlier today and welcomed the youngster to the club, he said; "We’re really pleased to have Callum on board, he is a highly rated at Walsall where they have high hopes for him. He is a tough tackler who fits into the mould of what we want, and I know he will bring some added steal and balance with his left foot."