Born on 2 February 1985 as the youngest of the family, Tharanga was born at Balapitiya General Hospital. His father Warushavithanage Bhadrasoma was a fish market dealer. His mother R.J Padma is a housewife and Tharanga has one elder brother Nuwan Tharanga and one elder sister Kumesha Manori. Though his brother used to enjoy swimming, Tharanga chose cricket at the younger age. He first attended Devananda College, Ambalangoda, and passed grade 5 scholarship in 1995. Since then, Tharanga had his secondary education at Dharmasoka College, Ambalangoda until ordinary level. However, with many cricket tours, he could not complete education towards advanced level. He started his cricket career as a teenager at his school.

Having played for Nondescripts since the age of 15, he played for Sri Lanka's under-15, under-17 and under-19 squads. He had a successful under-19 World Cup in 2004 with successful innings of 117 and 61 in successive games. He was sent by the Sri Lankan cricketing board to play league cricket for Loughton Cricket Club in Essex.

Tharanga's Sri Lankan call-up occurred on July 2005 when Sri Lanka was devastated, and after his family home was washed away by the 2004 Tsunami tragedy, where only the foundation of the house was left. His equipment, which was also washed away, was replaced by Kumar Sangakkara. Tharanga graduated to the "A" team and in July he was selected for the full squad.

In March 2018, he was named in Galle's squad for the 2017–18 Super Four Provincial Tournament. The following month, he was also named as the captain of Galle's squad for the 2018 Super Provincial One Day Tournament. He was the leading run-scorer in the tournament, with 396 runs in six matches.

In August 2018, he was named as Colombo's vice-captain for the 2018 SLC T20 League. In the opening match of the tournament, he scored 124 not out, with Colombo going on to beat Galle by 90 runs. He was the leading run-scorer for the tournament, finishing with 414 runs in six matches, including another unbeaten century in the final.

On the 2006 tour of England he really began to develop, particularly in the one-day game, scoring over 300 runs in Sri Lanka's 5–0 whitewash of the hosts. In addition, Tharanga is also well known for taking part in a record-breaking first wicket partnership with Sanath Jayasuriya in the final match of this series. He finished off with 109 off 102 balls, and played a pivotal role in completing the whitewash against England in England for the first time.

Tharanga lost his form in the 2007 World Cup scoring only one half century (against New Zealand) he then continued his poor run of form in the home series against England in 2007 where he failed to contribute and often fell before the 10th over often resulting in a middle-order collapse. Subsequently, he lost his ODI place to Malinda Warnapura and his test place to Michael Vandort but he remains within the squad.

However, in the 2011 World Cup, he is back to performing remarkably. In the quarter-final game against England, his partnership with Tillakaratne Dilshan, wrapped up the game, each acquiring centuries. His strong form has returned him to the opening position in the strong Sri-Lankan batting line up. He has also come in for special praise from Jayasuriya, one of the legends of cricket, saying that he could be the next captain of the Sri Lankan cricket team.