Mario Balotelli's agent Mino Raiola has revealed that the striker will not be leaving Anfield this summer.
Graham Dorrans has signed a two-year deal with Norwich City following a successful loan spell with the club.
The 20-year-old's current deal with Los Blancos was due to expire next June but the new agreement commits him to the club until 2017.
Just moments after it was confirmed on the club's official website, the player declared his delight at the news with a message on Twitter.
He said: "Very happy to have renewed my contract and to play for the best team in the world. I will give everything for this badge."
Jese, born in the Canary Islands, joined Real Madrid's academy aged 14.
He helped the club to promotion to the Segunda Division A, Spain's second tier, in 2011-12 and finished top scorer in the division last season, with 22 goals.
He has just played just once for the first team, in a Copa del Rey tie with Ponferradina in December 2011, but has been promoted to the first team for the coming season.
Jese, who can play on either wing, as a centre-forward or behind the striker, has represented Spain at under-19 and under-20 level.
He was part of the under-19 side which won the 2012 European Championships in Estonia and finished top scorer in the tournament. He hit five goals at this summer's under-20 World Cup in Turkey, where Spain were eliminated at the quarter finals stages by Uruguay.
According to reports in Spain, Jese will double his wages to earn around E1.2m per season, while a prohibitively large buy-out clause has also been inserted into the contract to deter interest from rival clubs.