Gallagher's move from Chelsea appeared off after a swap involving Samu Omorodion, now with Porto, fell through.
The England midfielder recalled those final days of the summer market when speaking to AS today: "I think it was during the Euros (the first contact). Around those weeks.
"A few months before I could close the transfer and sign the contract, these kinds of things take time. I always felt very loved by Atlético from the beginning and that made me feel very special. I am very excited and happy to be here.
"Yes, (Kieran) Trippier was with me at the Euros and we spent time together every day. We talked a lot about Atlético. He helped me a lot when it came to making the decision to come. He only had good things to say."
On spending six days in the Madrid hotel before having to return to London on Chelsea's orders, Gallagher continued: "It was stressful. I was in Madrid, ready to sign and become a new Atlético player. All I wanted was for it to be done so I could start training and be part of the team.
"All big transfers can get complicated and that's what happened with mine. But I always had the confidence that it would work out, because I knew how much Atlético wanted me to be here and how much I wanted to end up as a red-and-white. I always had the confidence that it would work out. Luckily it ended up happening and everything was perfect.
"Before the return trip I had a meeting with Cholo. He told me not to worry, that everything would be fine. He gave me a lot of peace of mind, because he told me: 'We are going to make sure we sign you, the only thing you have to do is be ready when you return to Madrid'.
"I returned to Chelsea, trained hard and when the deal was done I was ready to return to Madrid and put myself at Simeone's disposal."