The attacking midfielder, 19, is the son of former Manchester City and Arsenal defender Kolo Toure.
Toure Snr is now back with City as manager Pep Guardiola's No2.
Meanwhile, son Yassine joins Altrincham after spells in Celtic and Leicester City's academy.
Altrincham manager Neil Gibson said: "Yassine has a lot of potential. He has a huge amount of physical prowess. He is very strong, and, in one-on-one duels, he is quick, pacey.
"There is an area of his game that needs tidying up and he needs to learn men's football, so we are looking to give him some game time with other clubs, be it loan or dual registration.
"We will work with him over the next few months to try to improve him to a point where he can compete for a first-team place.
"He is still only young, and he has a good pedigree in terms of his time at Wrexham. His attitude in training has been fantastic.
"He has worked really hard, and he looks like someone who, over the next six to 12 months, we could mould into a good National League footballer."