The 51-year-old German joined the team in his role at the end of 2015. He'd previously worked in management roles at QuickStep and at T-Mobile, with the latter later morphing into Team Columbia and HTC.
A Dimension Data team statement released on Monday said that Aldag's departure was "an entirely amicable step, mutually decided on with a sense of gratitude for the past and heart-felt wishes of good luck for the respective futures".
Team principal Doug Ryder added: "Rolf's wide knowledge of the sport, which he was always willing to share, his skilled engagement with our partners and the implementation of systems and structures, together with his belief in the core ideal of the team – in that we are changing lives through bicycles – sees him depart as a valued member of our team's story. We wish Rolf and his family all the very best in the future."
Aldag's parting words mainly concentrated on his memories of the team's goal of supplying people in Africa with bicycles through the Qhubeka charity.
"After working productively for four years with the team, for me the bike handovers to South African kids at training camps in Cape Town will forever be one of the most emotional and memorable moments in my career," Aldag said in the statement. "And so I will continue to deeply root for the team's success in what it hopes to achieve, on and off the bike."
While the team's charitable ventures have been a great success, Dimension Data have struggled to get results over the past couple of seasons, winning just seven races in 2018 and only seven so far this season, with Edvald Boasson Hagen and new signing Giacomo Nizzolo, in particular this year, being heavily relied upon for bunch sprints as Mark Cavendish has struggled to recover from the Epstein-Barr virus the British sprinter's suffered with for the past two years.
Cavendish was given the all-clear as having medically recovered from the virus in May, but his non-selection for this year's Tour de France saw Aldag publicly voice his disagreement with that decision, making it clear that he would have included Cavendish if it had been his choice.
"It's no secret I wanted him here," Aldag said at the Tour in July. "I think it would suit our strategy, but ultimately it's a team-owner decision.
"It's within my remit to select the team, which I did," he said. "I wrote down eight names and Mark was included. And the team owner [Ryder] has the right to overrule me, which he did, and that was about it. And now we have eight athletes here who have done nothing wrong and deserve full support from everybody."
Ryder, meanwhile, said that the eight-rider selection was a team decision.
"There was a difference of opinions, but when you add all of those opinions together with the conversations that we had internally and all the information we have, and the route, the team felt that we've selected the best team for this year's Tour de France," said Ryder in July.
Aldag rode as a professional for 15 years, with the last 13 of those being for Telekom/T-Mobile. In 2007, he was one of a number of former T-Mobile riders who admitted to having used EPO while racing in the 1990s, and T-Mobile pulled out of sponsoring the team at the end of the 2007 season, after which the outfit became Team High Road until sportswear company Columbia stepped in as the team's new main sponsor ahead of the 2008 Tour de France.
The team later became HTC, but despite its success – particularly through star rider Cavendish – it shuttered its doors at the end of the 2011 after team owner Bob Stapleton was unable to find a new head sponsor.
Aldag later worked with Cavendish again at QuickStep – from 2013 to 2015 – before both men joined Dimension Data in 2016 when it stepped up to WorldTour level.