Marcos Rojo will become a Manchester United player and sign a five-year contract, subject to a medical, after the Argentina defender’s complicated third-party contractual position was finally untangled on Tuesday night.

Sporting Lisbon confirmed via their official Twitter account that the 24-year-old will move to Old Trafford, with the Portugal winger Nani moving back to his former club on a season-long loan: “#mufc has reached agreement with Sporting Lisbon to sign defender Marcos Rojo, subject to a medical and personal terms. A further announcement will be made when the process is complete.”

Rojo’s expected arrival means United have finally signed another player after Luke Shaw and Ander Herrera were bought in June for a combined £55m. The Argentinian is believed to have cost around £16m.

United faced particularly complicated negotiations due to him having more than one third-party entity with part ownership that had to be satisfied before the deal could be completed.

With club sources characterising the deal as among the most intricate of United’s recent transfers – the Doyen Sports Investment player fund are understood to have had a significant financial interest in Rojo – there is relief at Old Trafford he will become the first player bought who was identified solely by Louis van Gaal since he became manager in the close season.

Although the Dutchman signed off the deals for Shaw and Herrera, both players had been picked by his predecessor, David Moyes. While United had remained confident Rojo would become their third signing of the summer, the player appeared hasty when discussing the transfer with a radio station in his native Argentina as a fait accompli on Monday. Rojo described the 20-times champions as his “dream” club.

In the interview with the Argentinian radio station Continental, Rojo had indicated his move to United was completed. “It’s a dream to play at Manchester United and I am very proud of having the chance of working with [Louis] van Gaal,” he said. “I spoke with Juan Sebastián Verón about Manchester United when we were at Estudiantes. I have always liked English football and I should adapt to this new playing style easily.”Of his recent refusal to train with Sporting to try and force the transfer through, Rojo added: “There was a misunderstanding, I never wanted to do something wrong at Sporting as I have always been very thankful to that team that gave me many chances for playing in Europe.

“If I made a mistake I have already apologised because I didn’t want to hurt the feelings of anyone at the club.”

With Shaw out for around four weeks due to a hamstring injury, if he does arrive Rojo may slot straight into the team at left wing-back or as the left-sided central defender in Van Gaal’s 3-5-2 system. Rojo played left-back in Argentina’s run to the 2014 World Cup final, which the nation lost to Germany.

Although Rojo’s arrival is viewed now as a formality, this contrasts with any potential move for Real Madrid’s Ángel di María. Sources at United say neither Van Gaal nor any other executive has had any contact or discussions with the player about taking him to Old Trafford.

The situation could change as the1 September transfer deadline is less than two weeks away. Paris Saint-Germain, the French champions, remain hopeful of landing Di María, this time on a loan deal after a permanent move fell through due to the fee demanded by Real Madrid.