Dernbach was born in Johannesburg, South Africa to a South African father and an Italian mother and has used an Italian passport. He moved with his family to England in 2000 when he was 14. In South Africa, his preferred sport was rugby union, but he began to develop as a cricketer in England. After bowling at an under-15s net session at Surrey, he quickly moved through the age groups.

In 2010, Dernbach was selected for the England Performance Programme tour of Australia and subsequent England Lions tour of the West Indies where they participated in the domestic Regional Four Day Competition. In the latter, he took 19 wickets at an average of 15.63, making him the leading English bowler.

His consistency and regular wicket-taking for Surrey was rewarded with a place on the 2011 England Lions tour to the West Indies, before a late call-up to England’s 2011 World Cup squad made him the first Surrey youth academy graduate to secure recognition at this level. He continued to perform well for Surrey whenever available. His 2011 season was capped with a Man of the Match performance in the CB40 Final, where his 4/30 helped lift Surrey to victory.

Dernbach was a member of the England ODI squad for their match against Ireland in August 2011.

In the 2012 ICC World T20, he and Steven Finn equalled the tournament record for the highest 10th wicket partnership.

Dernbach was effective in Surrey’s successful T20 campaign in 2013, and was the side’s leading wicket taker with 18 wickets (at an average of 16.44) as Surrey reached the Finals Day at Edgbaston for the first time since 2006.

He was also named in the T20I XI by Cricinfo for his performances in 2013.

He announced his retirement from international cricket in July 2019, five years after his last T20I appearance.