Radamel Falcao has completed the formalities of his move to Chelsea and will link up with his new club on their pre-season tour of North America, according to the Colombian striker’s family.

Falcao’s uncle and father both confirmed on Tuesday night that a deal had been signed with the London club, believed to be a one-year loan from his French club, Monaco, with an option to make the move permanent next summer. This ensures the 29-year-old will remain in the Premier League next term following last season’s similar spell at Manchester United.

Chelsea are yet to officially announce the signing but had held almost three weeks of talks with Falcao’s representative, Jorge Mendes, and Monaco in an attempt to reach a compromise over the player’s £265,000-a-week pay package and loan fee. Agreement was eventually reached late last month, with the champions expected to pay the striker nearer £180,000 a week with a loan fee negotiated at around £4m for his services.

José Mourinho, another Mendes client, has previously admitted to wanting to “help Falcao get back to his level” following the serious knee ligament injury suffered in January 2014, which ruled him out of last summer’s World Cup, while the forward had stated he was keen to extend his stay in the Premier League after United opted against making his move permanent for £43.2m. He scored only four goals in 26 appearances for Louis van Gaal’s side last term.

The player’s father, Radamel García, who was himself a professional footballer, confirmed a deal had been completed in an interview with Caracol TV on Tuesday. He suggested Falcao would report to Chelsea’s pre-season base in Montreal, Canada on 19 or 20 July having been granted extra time off after the Copa América.

Falcao’s uncle, Herbert King, who is currently with the striker on holiday in Colombia, also confirmed to The Guardian that a contract had been signed.

Once one of the most feared strikers in the world, Falcao has endured a wretched time since rupturing his cruciate ligament in a French Cup tie 19 months ago. His spell at United ended with a solitary shot on target in his final 12 Premier League appearances, and an appearance for the club’s development side against Tottenham Hotspur as Van Gaal desperately sought to repair the player’s shattered confidence.

After the option to make the move permanent was passed up, Falcao was named as Colombia’s captain by the manager José Pekerman for this summer’s Copa América in an attempt to restores his confidence. But, after failing to make his mark in the opening three games of Colombia’s campaign, El Tigre was dropped to the bench as Los Cafeteros crashed out of the tournament on penalties to Argentina in the quarter-finals. Falcao appeared as a second-half substitute and converted his spot-kick, but finished the Copa América having attempted just one shot in open play.

Falcao will spend the next few days with his family in Colombia before joining Chelsea on their pre-season tour of North America, where they will play Barcelona, Paris Saint-Germain and New York Red Bulls in the International Champions Cup later this month.