The son of a carpenter from Moratuwa, Dananjaya studied at Panadura Mahanama Navodya Vidyalaya, Panadura. He married his longtime partner Nethalie Tekshini on 22 August 2017 just two days before his recall to the ODI team for second ODI against India. The wedding was celebrated at Ramadia Ran Mal Holiday Resort, Moratuwa and two spinners Rangana Herath and Ajantha Mendis signed as witnesses.

He was selected to play for Wayamba United in the inaugural Sri Lanka Premier League. In only his second match for the franchise, he took 3–18 against Nagenahira Nagas, consistently disturbing the batsmen with his flight, googly and other variations.

In the 2013 IPL auctions, Dananjaya was sold to the Chennai Super Kings for his base price of $20,000. In January 2018, he was bought by the Mumbai Indians in the 2018 IPL auction.

In March 2018, he was named in Galle's squad for the 2017–18 Super Four Provincial Tournament. In August 2018, he was named in Colombo's squad the 2018 SLC T20 League.

Officially a left-hand batsman and an off-break bowler, he is said to have seven variations, including the leg-break, googly, carrom ball, doosra and his stock off-spinner that had impressed national team captain Mahela Jayawardene so much in the nets as to make Jayawardene request him to be fast-tracked into the national squad. Dhananjaya had at that point played no first-class, List A, T20 or even U-19 cricket. This in turn led to controversy as his selection was questioned by the media on the basis of a net performance.

This in turn led to a place in the final squad for the 2012 ICC World Twenty20. He made his debut international appearance at the age of 18 against New Zealand at Pallekele in a pool match of World Twenty20.

He was hit on the face by a full-blooded drive from New Zealand opener Rob Nicol, with the ball going through his hands to strike the left side of his face. X-rays and MRI scans revealed that he had suffered a fracture on his left cheek bone as a result of the blow and did not play in the pool match against West Indies.

Dananjaya was recalled in to the ODI squad after five years for the Zimbabwe tour in 2017. In the first match of the series, he took his maiden ODI wicket by dismissing Craig Ervine. He took his maiden ODI five-wicket haul on 24 August 2017 against India at Pallekele Cricket Stadium. His fifer took in the spa of 13 deliveries, which is the best for a Sri Lankan in ODIs as well. He bewildered the Indian batsmen. However, India won the match by 3 wickets at the end and Dananjaya's bowling figures of 6 for 54 stands as the best bowling figures by a Sri Lankan in a losing cause.^[16][17] Despite the loss, he awarded man of the match for impressive bowling performance.

On 13 October 2017 against Pakistan, Dananjaya scored his maiden ODI fifty. His score of an unbeaten 50 off 72 balls did not help Sri Lanka to win the match, but helped to reach 200 mark in total.^[18]

In 2018, Dhananjaya was named to Sri Lanka's Test squad for the tour of Bangladesh