The company, which was founded in Denmark in 2001, aims to raise £100 million, in a move that is expected to value it at between £700m and £900m.
It will become the latest business to make its stock market debut, after recent launches from Poundland, Pets at Home, online white goods retailer AO and fashion website boohoo.com in recent weeks.
Just Eat's chief executive David Buttress said: "I'm very pleased to be bringing Just Eat to market following several years of strong growth and expansion.
"Just Eat brings together tens of thousands of local takeaway restaurants globally and processes millions of online orders monthly, which I believe makes us one of the most exciting global growth companies in Europe."
Just Eat operates in 13 countries, including Denmark, France, Canada, Ireland and Spain. Its network covers more than 36,000 takeaway restaurants.
It said its strong financial performance continued last year, with revenues up 57.3% to £80.4m and underlying earnings increasing 69.9% to £30.2m, compared to 2012.
Separately, the company said it had added BSkyB finance director Andrew Griffith and former Asda customers services director Gwyn Burr to its board as non-executive directors.