The 35-year-old joined Inter on a free transfer last summer and has gone on to play a major role in the Nerazurri's Scudetto triumph.
Speaking to Sky Sports, Young said: "It became a massive decision. I was club captain and going into my 10th year, but the club was evolving and changing. Ole was there and he was doing really well. It was a decision I had to make in footballing terms.
"I knew how fit I was and I knew I could play week in and week out. A lot is said about age, more so in England than in other countries. If you know how fit you are then there is no problem.
"I sat down with Ole and asked about my chances of playing. He was truthful, I understood what he was saying, it was going to be limited. There was a contract put on the table.
"But I didn't want to be an afterthought, I did not want to sit there another year and play a bit part. I know I can get up and down like I was 20 years old.
"Being told by one of the biggest teams in the world like Inter Milan that you are going to play every week, I told my representatives 'let's get the deal done'."
Asked if he could have remained at Old Trafford had the contract offer came earlier, he replied: "Possibly. But we are not to know.
"I was there and sat down and spoke to Ole, he wanted me to stay. It was a decision I had to make. I felt like I had a lot left in me.