Cohen was born in Tel Aviv, Israel, and is Jewish. He started his career in Maccabi Tel Aviv's youth team where in 2001–02 he won the double. His first game in the Israeli Premier League was in November 2002 during Maccabi's 1–0 win over Bnei Yehuda Tel Aviv, when he came on as a substitute. He scored his first goal against Maccabi Petah Tikva in a 2–1 in the Toto Cup, where he scored the winning goal. On 11 January 2007 Cohen moved to Maccabi Netanya.
On 1 January 2008 he transferred to English club Bolton Wanderers for a fee of £39,000. He made his Bolton debut in the 1–0 FA Cup defeat to Sheffield United, wearing the squad number 25, previously occupied by Abdoulaye Faye. His first Premiership goal was scored on 2 March 2008 in a match against his father's former club Liverpool at the Reebok stadium, which ended in a 3–1 win for Liverpool. The 25-year-old made 11 appearances in his first season in English football. In the 2008/2009 campaign, Cohen played a peripheral role for Bolton Wanderers this campaign with a longstanding thigh injury keeping him out of action for over five months. The Israeli man eventually returned to the first team fold in the final couple of months of the season, earning his first start against Aston Villa at the Reebok Stadium on 25 April. Cohen stole all the headlines with a vibrant midfield performance and capped off the afternoon with a neatly taken equaliser to earn Bolton a vital point. He celebrated his goal by saluting his friends and family who were sat in the West Stand after he had been handed a 'lucky shekel' to put down his sock. Cohen expressed hope that his injury problems would be behind him and that Wanderers fans would see more of his footballing talents in the 2009/2010, saying "It's been very frustrating because it's not easy for a football player to be injured. But that is football and you need to live with that. Now hopefully I won't be out anymore while I'm with Bolton". Cohen was released by Bolton Wanderers at the end of the 2010–11 season, after three and a half years at the club.
On 8 August 2011, Cohen signed a 4-year deal with Israeli Maccabi Haifa. He rejected an offer from Greek side Panathinaikos in order to play in Israel where he can be closer to his family. Tamir earned €300,000, the highest salary in Maccabi Haifa.
Cohen holds an Italian passport in addition to his Israeli one owing to his Italian ancestry. His citizenship of a European Union country gives him the option of playing for an EU football club without having to be classified as a foreigner. He is the son of Maccabi Tel Aviv and Rangers player Avi Cohen. Following his father's ultimately fatal motorcycle accident in December 2010, he flew to Israel to be at his father's bedside. On 24 April 2011, Cohen emotionally celebrated by taking off his shirt to reveal a picture of his father after scoring the winning goal in Bolton's 2–1 victory over Arsenal. Cohen is also the nephew of the former association football playerVicky Peretz and the cousin of Peretz sons – Adi and Omer Peretz.
