The new kit, which was launched at midnight on Saturday, marks the beginning of a 10-year partnership between the Premier League club and the German sports manufacturer and sees United end their 13-year association with American sports company Nike.
The deal, which was announced in July 2014, will see United earn a minimum of £750m in revenue over the duration of the deal.
United will now earn in excess of £100m a season from kit sponsorship alone, with the club receiving £47m a year from American car manufacturers Chevrolet.
The deal pairs United with adidas for the second time in their respective histories, with adidas designing the Reds’ kit between 1980 and 1992.
United will don their new strip for the first time in this season’s Premier League curtain raiser against Tottenham at Old Trafford next Saturday.
The design of the new kits has been a personal passion for adidas designer Inigo Turner, who is a lifelong Manchester United fan.
“At adidas we have been on a real journey in creating these new kits for Manchester United,” Turner said. “This landmark sponsorship is not the first time we have partnered with the club and it is with these iconic kits of the past that we drew our inspiration from.”
“We have aimed to break expectations by re-engineering simple but impactful design features such as the classic v-neck collar and the iconic three-stripe detailing down the arms as our commitment to giving Manchester United a truly ground breaking kit for the 2015/16 season.”
Manchester United Group managing director Richard Arnold added: “Everyone at United is very proud of the shirt’s classic design, which draws upon the Club’s iconic kits of yesteryear. Manchester United and adidas have a long and illustrious history in football, both leading the way in innovation and performance.
“The design of the 2015/16 kit will not only appeal to our loyal supporters, it will also showcase adidas’ expertise in creating state of the art performance products for the football industry.
“We look forward to sharing the designs for our complete adidas range with fans via our 100m social media connections, as well as seeing them within the stadium and on the streets, creating a new classic design culture, opening a new chapter in Manchester United’s history.
“We are proud to welcome adidas back to the Manchester United family and look forward to a successful and exciting future together.”