The 40-year-old was with the Danish team for two years having called time on his career as a professional rider in 2008.
“I have decided to move on. More family time,” he tweeted.
“Have never witnessed a more dedicated passionate group of people,” he added. “Bjarne (Riis, Saxo-Tinkoff owner) is simply special. The man is a visionary, great for the sport.”
Gates did not disclose what his future plans are, but did hint that had something in the pipeline.