The £20m will be the first of two fundraising rounds in which the company intends to raise between £70m and £100m.
Gamucci, whose products are sold in WH Smith and Waitrose, expects its e-cigarette sales to reach £10m in this financial year.
Analysts from Canaccord Genuity earlier this month said they expect the global market for e-cigarettes to rise from £1.3bn to £1.9bn this year.
The investment bank said it expects e-cigarettes will be the “most significant development in the history of the organised tobacco industry”.
Gamucci was founded in 2007 by brothers Taz and Umer Sheikh, and the company now operates in 20 countries.
This year Gamucci has recruited five former tobacco executives into senior positions, including new chief executive Tony Scanlan who has 17 years of experience with Rothmans International.