The 56-year-old former manager of English Premier League club Fulham, who helped France win the 1984 European championship, held a news conference in Shanghai on Sunday after sealing the deal with club owner Zhou Jun.
Anelka's deal was reported to be in the region of $300,000 a week for two years but Tigana said he was not moving to China for the money.
"I could have gone to England or to Turkey," he said, without giving any financial details of his move.
"I am privileged to be here. I found a new challenge here. This is not a financial choice - it is a sport and life decision."
Tigana, who quit as coach of French side Bordeaux this year, praised Anelka but would not respond to a suggestion that former Real Madrid midfielder Guti could also follow them to China.
"Firstly, Anelka's signing has been arranged before my arrival," Tigana said. "He is a very talented footballer who will bring a lot to the club. We cannot mention other names at the moment because we have not signed any other players."
Fellow Frenchman Philippe Troussier is also managing a Chinese club, Shenzhen Ruby in southern China, while former Japan coach Takeshi Okada was appointed manager of Hangzhou Greentown on Thursday.
Shanghai Shenhua, backed by internet tycoon Zhu Jun's financial muscle, are showing they can compete with anyone in the transfer market and are now 72nd in the FIFA world rankings.
They finished 11th in the league last season.
