Everton have completed the transfer of James Rodríguez from Real Madrid for around £20m with the Colombia international signing a two-year contract with the option of a third.

The 29-year-old joins Allan as the second major part of Carlo Ancelotti’s midfield rebuild and is believed to have accepted a pay cut on his £140,000-a-week wage to be reunited with his former manager at Real and Bayern Munich.

Rodríguez was in the final year of his contract with the Spanish champions and started only five league games under Zinedine Zidane last season. He cost Real £63m when moving from Monaco after the 2014 World Cup, when he won the Golden Boot while helping Colombia to reach the quarter-finals, but spent two seasons on loan at Bayern from 2017 after losing his regular starting role.

“I’ve come here to try to improve, to get better,” said Rodríguez. “I’ve also come here to help the team to win, to play good football – entertaining football. I’m convinced, with Carlo and his technical staff, we can achieve big things and one of the big reasons [for signing] was the presence of Carlo Ancelotti. I have enjoyed some great times with him previously at two different clubs. That was a massive reason to come here.”

Everton, who have the option on the third year of the contract, have been working on the deal for several weeks and believe Rodríguez’s transfer will accelerate their international growth plans. The former Porto playmaker has a social media following of almost 100 million and the club broadcast his arrival in Bogota and Miami, where Everton are considering opening its first international office in the US.

Rodriguez said: “I’m a winner, I’m a real winner. I can see the plans here, the project here is very serious. Everyone means business. I think the seriousness and determination to win trophies can lead to silverware.”

Everton signed the Brazil international Allan from Napoli for an initial £22m on Saturday and hope to add a third midfielder before starting the Premier League season at Tottenham. The club have agreed a fee of around £20m with Watford for their long-term target Abdoulaye Doucouré.