Twenty-one-year-old Laird came through the Red Devils' youth setup but only ever managed two appearances for the first team after graduating from their academy.
Both of Laird's senior games came in the 2019-20 Europa League, where he played the full 90 minutes on his debut in a 2-1 group-stage defeat to FC Astana.
The right-back was subsequently given his first taste of Old Trafford football in their following continental game - a 4-0 win over AZ Alkmaar - but he failed to make another matchday squad for Man United.
Loan spells at MK Dons, Swansea City, Bournemouth and Queens Park Rangers followed for Laird, who featured regularly for the latter last term with one goal and two assists in 32 Championship appearances.
Having proven himself at Championship level, the former England Under-19 international has now completed a permanent move away from Manchester to join up with Birmingham.
"All at United would like to pass on our sincere best wishes to Ethan and we'll be tracking his progress at his new club after successfully coming through our Academy and always being a popular figure at Carrington," Man United said in a statement.
Meanwhile, midfielder Galbraith is officially out of contract at the end of June and will be dropping down to League One to turn out for Leyton Orient on a two-year deal.
The Northern Ireland international left Linfield in 2017 to join Man United's academy ranks and also made his solitary first-team appearance against Astana in the 2019-20 Europa League.
Galbraith came off the bench for the final two minutes of that encounter, and he has since gleaned senior experience with Doncaster Rovers and Salford City in League One and Two respectively.
Galbraith was a key player for Salford last season with four goals and three assists in 32 matches, helping his side reach the playoffs, where they lost to Stockport County on penalties in the semi-finals.
"We would like to wish Ethan the very best of luck at his new club and thank him for his service with the Reds, as he is another player the Academy can be extremely proud of," Man United said of Galbraith, who hailed the influence of head coach Richie Wellens in his decision.
"From playing against Leyton Orient last season, I got a good feel for the side here, and the style of football," Galbraith told the official Leyton Orient website.
"Richie was a big factor, I know how he likes to play, and how he wants to get the best out of his players, so it was a great fit."
Galbraith and Laird become the latest Man United youngsters to head for the exit door after Di'Shon Bernard and Zidane Iqbal, the latter of whom has signed for Utrecht on a permanent deal.