The trio of captain's picks had been part of a five-man shortlist for selection to take on the United States, with Luke Donald and Francesco Molinari the two to miss out.
Gallacher, Poulter and Westwood join automatic qualifiers Rory McIlroy, Henrik Stenson, Victor Dubuisson, Jamie Donaldson, Sergio Garcia, Thomas Bjorn, Justin Rose, Martin Kaymer and Graeme McDowell in the defending champions' squad.
World number 33 Gallacher was unfortunate to miss out on an automatic Ryder Cup berth, having finished one shot short of the second place he needed at the Italian Open on Sunday.
However, McGinley has now offered the 39-year-old a reprieve, and Gallacher will be the only Scottish representative at his debut Ryder Cup at Gleneagles.
Asked what the picks' reactions were upon being told of their selection, McGinley said: "Excitement is the word.
"Stevie Gallacher I said 'go and have a drink to celebrate' and he said 'is that ok?'.
"I have played a home Ryder Cup and I know what it is going to feel like and how proud he will be.
"With Lee [Westwood] there was a real sense of pride he had made another team, very gracious and very humble, and Ian Poulter is a bundle of energy, you can feel the energy coming down the phone."
McGinley also revealed Donald had not been expecting to be omitted.
"He was very disappointed," he added. "He is a former number one in the world. The first ever shot he hit in the Ryder Cup I was his partner.
"He told me he publicly backed me to be the captain. Even though I hadn't picked him he told me he backed me and his last words were 'Go Europe'.
"I think that says a lot about Luke. He wasn't expecting [to be left out]. He was very disappointed."
Poulter has been one of the biggest Ryder Cup characters in recent history and has produced the results to back it up.
The Englishman has struggled for form this season but his record at the transatlantic event is impressive - winning 12 points from a possible 15.
Former world number one Westwood, meanwhile, is another seasoned campaigner.
Having made his debut in 1997, he has now featured eight times at the showpiece, with a record of 18 points and six halves from a possible 37.
The 2014 Ryder Cup begins on September 26.