Ten Hag was officially confirmed as the new Red Devils manager at the end of April, but he did not officially speak about his new role at Old Trafford until the end of the Eredivisie campaign, which saw him lead Ajax to another league title.
The Dutchman was in attendance for last Sunday's 1-0 defeat to Crystal Palace in the Premier League before holding his first press conference as Man United boss on Monday.
A number of managers were linked with the position at Old Trafford, including Paris Saint-Germain's Mauricio Pochettino, Spain's Luis Enrique and Leicester City's Brendan Rodgers, but Murtough has said that Ten Hag was the club's number one choice due to his vision.
"He showed passion, energy and enthusiasm for the challenge," Murtough told a meeting of the club's Fans' Forum.
According to the Man United football director, Ten Hag set out a "long-term vision to build a successful, exciting team" during his discussions with the 20-time English champions.
Meanwhile, Murtough claims that the 52-year-old was the head coach "most closely aligned with the identity and aims of Manchester United," relating to attacking football and bringing through young players.
Murtough also confirmed that the club were planning to develop their training facilities, with former Red Devils captain Gary Neville among those to recently criticise the training complex.
"It's all about making sure we are creating the right environment and culture in which players can perform to their maximum potential," the football director added.
Ten Hag has allegedly decided to undertake an internal review at Man United, meanwhile, in order to determine which staff will remain at the club this summer.
Ten Hag will have a break before the start of Man United's pre-season, with the Dutchman revealing that the players not involved for their countries next month will be due back on June 27.
The club have also now confirmed their pre-season plans, travelling to Bangkok, Melbourne, Perth and Oslo ahead of the 2022-23 Premier League campaign, which begins on August 6.
Man United will face Liverpool, Melbourne Victory, Crystal Palace and Aston Villa before visiting Oslo to take on Spanish giants Atletico Madrid at the end of July.
The 20-time English champions lost their final two Premier League matches of the season to Brighton & Hove Albion and Palace but still managed to secure sixth in the table, which will see them compete in the group stage of next season's Europa League.
There will be additions at the club this summer, meanwhile, with Barcelona's Frenkie de Jong, Villarreal's Pau Torres, Ajax's Jurrien Timber and Benfica's Darwin Nunez all believed to be leading targets.