Youth-team products Sam Johnstone, Tyler Blackett, Michael Keane, Reece James, Jesse Lingard and Will Keane all made the cut, but there was no room for James Wilson and Tom Lawrence, who made their first-term debuts at the end of last season, or Nick Powell.
United had announced earlier this month that stars like Wayne Rooney, David De Gea and Juan Mata would travel to the US along with new signings Luke Shaw and Ander Herrera.
Robin van Persie, Javier Hernandez, Marouane Fellaini and Adnan Januzaj are still on holiday after the World Cup.
Michael Carrick is a notable absentee after undergoing ankle surgery on Thursday morning that could rule him out for the first two months of the season.
In his first press conference later in the day, Van Gaal said he would spend the next three or four weeks assessing the players he has at his disposal before deciding on potential new signings and departures.
United will play their first match of the tour against the Los Angeles Galaxy next Thursday before taking on Roma, Inter Milan and Real Madrid in the International Champions Cup.
If they make the final, they will play a fifth match in Miami on August 4.
The tour will be a big chance for the likes of Tom Cleverley, Darren Fletcher, Ashley Young, Shinji Kagawa and Nani to prove they deserve a future at Old Trafford.
The fate of Anderson and Bebe already appears to be sealed, though, after they were left out along with left-back Patrice Evra, who is expected to join Juventus.
Chris Smalling, Phil Jones and Jonny Evans will hope to stake their claims to be first-choice centre-backs following the departures of Rio Ferdinand and Nemanja Vidic.
Spanish midfielder Herrera, who joined United from Athletic Bilbao last month, is looking forward to the tour.
He told MUTV: "It will be a new experience for me because it will be my first time outside Europe. All the people have told me there is a lot of United fans in America and I can’t wait to play in front of them.
United later announced that Anderson’s absence from the tour was due to a calf injury sustained in training.
The Brazilian joined United in 2007 but has been an increasingly fringe figure at Old Trafford and spent the second half of last season on loan at Fiorentina.
"I am very happy and really enjoying being at the club and in the city. The first couple of weeks here have been great.
"Training has been good, similar to at Bilbao in that we train a lot with the ball. The coaches want us to have the ball and keep possession, which is great for the players."