After advising on the company’s $6.8bn (£3.32bn) acquisition of UK ferry operator P&O last year, both firms have scored roles on the IPO, which takes place two years after the exchange launched in 2005.
Last year DP World said it aimed to sell a 20 per cent stake in its business, hoping to raise $4bn (£1.95bn).
The flotation represents the largest of its kind in the Middle East to date.
The Clifford Chance team was led by partners Iain Hunter in Dubai and Michael Dakin in London.
Underwriters Merrill Lynch and Deutsche Bank are being advised by a Linklaters team led by capital markets partner Jason Manketo.