Louis van Gaal has bolstered Manchester United’s options by completing the signings of the Germany World Cup winner Bastian Schweinsteiger from Bayern Munich and the Torino defender Matteo Darmian. United’s manager is also trying to sign Southampton’s Morgan Schneiderlin before the club fly out for their summer tour of the US on Monday.

Bayern’s chief executive, Karl-Heinz Rummenigge, said he regretted having to sell the Germany captain but explained that Schweinsteiger “just wants to do something new at the end of his career … Bastian was an extremely deserving player for us. He has done great things. I can only wish him all the best with what will be an interesting task.”

It is understood that Bayern accepted a bid of around £15m for Schweinsteiger, with the 30-year-old offered terms worth £140,000 a week over three years.

Schweinsteiger, who had a year remaining on his Bayern contract, played under Van Gaal at the German club between 2009 and 2011, where they enjoyed a strong working relationship. He came through the youth ranks at Bayern, winning the Bundesliga title eight times. During a glittering career he made 536 appearances and won seven German Cups and, in 2013, the Champions League. At international level he has been a mainstay in Germany’s midfield since his debut in 2004, scoring 23 goals in 111 appearances, and is their fifth-highest capped player.

Joachim Löw, the Germany coach who led them to victory in Brazil last year, hailed the transfer via Twitter, writing: “He is an absolute leader and world-class player, who can make his mark on any team.”

A few hours after the deal for Schweinsteiger was agreed, Torino confirmed the sale of their 25-year-old full-back Darmian to United. He travelled to England on Friday after a fee, believed to be in the region of £12.7m, was agreed. A Torino statement said: “President Urbano Cairo would like to thank Matteo Darmian for the seriousness, commitment and professionalism demonstrated in these years. Torino FC wishes Matteo all the best for this amazing new experience.”

The moves, which follow the £21.5m signing of the Holland winger Memphis Depay from PSV Eindhoven, are a statement of intent by United, who are looking to re-establish themselves after seventh- and fourth-place finishes in their last two league campaigns.

Van Gaal has had an offer of £20m rejected for Schneiderlin, with Ronald Koeman, the Southampton manager, valuing the Frenchman at £27m. However, United believe the player could be acquired for closer to £25m.