Talks over a deal were at an impasse until Real made a new offer on Wednesday, with Vinicius understood to be appreciative of the fresh terms.
He joined Real from Brazilian side Flamengo in 2018 and signed a contract extension three years ago.
Real and his representatives have been in talks over a fresh deal for the past 18 months but he has now extended his stay at what he has previously called the club of his “dreams”.
He returned to the club on Monday for his first pre-season training session and medical assessment following his World Cup campaign with Brazil.
Vinicius has scored 128 goals in 375 appearances for Real across all competitions, while he has 13 goals in 54 caps for Brazil.
He has helped Real win two Champions League titles, three La Ligas and one Copa del Rey during his time at the club.
It is understood Arsenal would have accelerated their interest in the Brazilian if he had rejected Real’s terms but the Premier League champions must now look elsewhere as they target a left-sided forward.
Vincius’ contract extension comes on the same day Real announced the signing of Ivory Coast winger Yan Diomande from RB Leipzig for a fee worth up to £120m (140m euros).
Diomande is Real’s sixth summer signing under new head coach Jose Mourinho, joining Bernardo Silva, Ibrahima Konate, Denzel Dumfries, Marc Cucurella and Carlos Espi.
Real are also targeting Manchester City and Spain midfielder Rodri but now face competition from bitter rivals Barcelona.