The two companies, which are based in New York, had already formed a non-equity alliance in March last year.
Oasis has 35 employees and estimated billings of $41m (£29m). Clients include the Government of India Tourist Office and Toyota Motor Sales. Most recently, it won the Sharp Electronics account.
In other news, Japan's fourth-biggest advertising agency Tokyo Agency said it will postpone its listing on the Tokyo Stock Exchange until the autumn of 2003.
The company had originally planned to list its shares by the end of this year, but it has decided to postpone because it expects to post net losses of Y7bn (£40m) for the year that ended in March.
The losses were down to appraisal losses in its real estate holdings, and the group plans to improve its finances before the listing by selling its headquarters and other buildings.