Zaugg, currently at RadioShack-Nissan, is primarily a domestique who works for his team-mates, but won the Tour of Lombardy classic while at Leopard Trek in 2011.
The 31-year-old said he hopes to impress in both capacities at his new team.
"For me, I have already found new motivation to continue to give everything I have, to my captains and team-mates," he said.
"My impression is that Saxo Bank-Tinkoff Bank can offer me a fantastic working environment where I can be happy and feel appreciated.
"I also expect that I can develop myself as a rider, and I hope I can help the team get results - and why not also on a personal level."
Team owner Bjarne Riis said: "Oliver is one of those riders that every team needs. He is experienced, strong and wise, as he showed by winning an extremely tough race Tour of Lombardy last year.
"But he is also the loyal and devoted helper who gives everything he has for his team. I think he is a great asset to us in achieving our goals."