The Englishman was selected - along with Stephen Gallacher and Ian Poulter - to join the nine men who qualified automatically for the showpiece event, it was announced on Tuesday.
It will be the 41-year-old's ninth Ryder Cup appearance, having made his debut in 1997.
"I'm obviously delighted," he said. "The Ryder Cup has always been a massive thing for me and I was delighted to get the call from Paul.
"It was a long day [on Monday] but when Paul rang with the good news I breathed a sigh of relief.
"I've played a lot better in the last month and a half and I've been showing some form and giving Paul a reason to pick me.
"I'm delighted and honoured to be representing Europe again."
Gallacher, who has never featured at the Ryder Cup before, missed out on an automatic place in the 12-man squad by one stroke at the Italian Open at the weekend, but was offered a reprieve by McGinley.
"It's massive for me and my family," he beamed. "It's been a goal all my career to play in the Ryder Cup and I was delighted to get the call from Paul.
"On Sunday I had mixed emotions. I was delighted with the way I played but disappointed not to have made the team automatically.
"I knew there were other great players in with a shout of getting a pick, so I really didn’t know what was going to happen. I’m just glad it all turned out okay in the end."
Poulter has won 12 points from a possible 15 at the Ryder Cup and added: "I'm absolutely thrilled. To get the call was amazing. I can't wait for Gleneagles.
"It's a fantastic feeling and I’m proud to be a pick. The Ryder Cup means a lot to me and I can’t wait. It’s always difficult to make a Ryder Cup team and this one was no different.
"Paul had a very difficult decision with some fantastic players to pick from."
The 2014 Ryder Cup begins on September 26.