The trio join automatic qualifiers Rory McIlroy, Henrik Stenson, Justin Rose, Sergio Garcia, Martin Kaymer, Victor Dubuisson, Thomas Bjorn, Jamie Donaldson and Graeme McDowell in a 12-man team for the Sept.
26-28 matches against the United States.
Poulter, 38, the fierce, bulging-eyed competitor who inspired the remarkable “Miracle in Medinah” comeback victory two years ago, has had an injury-plagued season but a European team without him seems almost unthinkable.
Former world number one Westwood, 41, has played in the last eight Ryder Cups while 39-year-old rookie Gallacher will be making his debut in the biennial team event on home soil at Gleneagles, Scotland.
Among the players to miss out on a pick were former world number one Luke Donald, Italian Francesco Molinari, veteran pair Bernhard Langer and Miguel Angel Jimenez, England’s Paul Casey and Dutchman Joost Luiten.
“I’m a very lucky man to have such a variety of talent to choose from,” McGinley told a news conference at Wentworth on the outskirts of London. “There are some real quality players who haven’t made the team.
“But on the positive side I think we have three players who will add a lot to the nine who have already qualified and make the European team as strong as it needs to be to take on the might of America.”
McGinley said Gallacher, who almost displaced McDowell as the ninth automatic qualifier when he finished third at the Italian Open on Sunday, thoroughly deserved his selection.
“Stevie’s first words to me when I told him he was in the team were, ‘That’s brilliant wee man’,” added the 5-foot-7 (1.7-metre) Irishman.
“Of course there’s always a concern that he’s a rookie but I’m not afraid to pick a rookie if he’s good enough and there’s no doubt Stevie earned his place in this team.”
McGinley said he was particularly impressed with Gallacher’s display under pressure in Turin.
“His performances last week in particular had a big effect on me,” explained Europe’s captain. “Stevie played relatively poorly for three weeks in a row in America but came back and had a good performance in the Czech Masters and then played well last week.
“For me Friday afternoon was when he showed he really wanted to be a Ryder Cup player. To come home in 30 shots and get within touching distance of the leaders showed just how strong he is.”
Englishman Westwood will be making his ninth successive Ryder Cup appearance, only Nick Faldo (11), Langer (10) and Christy O’Connor senior (10) have played more for Europe.
“There was a real sense of pride when I spoke to Lee,” said McGinley who explained his decision by phone to most of the players in contention for a pick. “He was very gracious, very humble when he learned he would be on the team.
“Ian Poulter is a bundle of energy and you could feel the energy that was coming down the phone.”
McGinley said the calls to his three picks were easy, unlike those that were made to the players who missed out.
He described the conversation with Donald, who has never been on the losing side in four previous Ryder Cup appearances in 2004, 2006, 2010 and 2012, as very difficult.
“I was Luke’s partner when he played his first match in 2004,” said McGinley. “Every Ryder Cup he’s been involved in, I’ve been involved in as a player or vice-captain.
“I have forged a very strong relationship with him. He’s been an incredible performer over the years and his record is outstanding.
“He was very, very disappointed and rightly so. He said ‘even though you haven’t picked me I still back you to be a great captain’ – that says a lot about Luke,” said McGinley.
“He will go on to make many more appearances and it was a very, very difficult call for me to make but one I had to do in the interests of the European team.”
McGinley said Italian Molinari, who appeared in the Ryder Cup in 2010 and 2012, was another serious contender for a pick.
“We gave Francesco a lot of thought and, just like Luke, he was incredibly humble, incredibly accepting of my decision,” said the captain.
“I couldn’t have asked for two guys to have accepted my decision in a better way and it speaks volumes of them.
“I also called Bernhard Langer out of respect. He wasn’t in consideration for a pick but as a captain I played under, I want to have a chat with him,” added McGinley.
“I’ve left messages for him but haven’t managed to reach him yet…I’m interested to hear his views on a number of things.”
U.S. captain Tom Watson is scheduled to announce his three wildcards in New York later on Tuesday.
(Editing by Ed Osmond and Toby Davis)