Yesil, who had also attracted interest from Arsenal, shone in last year's Under-17 World Cup when he scored six goals in seven matches for Germany.
He has progressed through the youth ranks at Leverkusen and has been a prolific scorer for their under-19s.
Yesil is unlikely to go straight into Liverpool's first team squad as he's viewed as one for the future.
Just like Nuri Sahin, whose services Brendan Rodgers acquired from Real Madrid for a season-long loan this summer, Yesil has a Turkey and Germany connection. The 18-year-old youngster was born in Germany and has a Turkish descent. Sahin, while also born in Germany, plays for Turkey.
Yesil was the second-highest scorer at the 2011 FIFA Under-17 World Cup in Germany's journey to third place and won the Silver Shoe for his efforts that included scoring 6 goals. The Golden Shoe was won by Souleymane Coulibaly who scored nine in four games and currently plays for Tottenham, Liverpool's direct rival for fourth place in the League.
Bringing an 18-year-old in the past was often seen as a signing for the future, at least within the Liverpool and Anfield premises. Chances were rarely thrown out to youngsters, especially if they were not from the defending department. Rodgers' outlook with a first League start given to Raheem Sterling against the Champions this past Sunday has changed all that.
It may actually be possible that Yesil does compete for first team's chances with Adam Morgan for the spot of the fourth genuine striker. As crazy as it might seem, it may actually be the exciting truth rather than the bitter. And again, as with all Rodgers' signings this season, Yesil has pace.