The appointment ends the Dutch retail giant's 12-month hunt for a global head of comms, following the departure of Sharon Christians.
Ahold head of PR Nick Gale refused to comment on the appointment, citing the company's market disclosure obligations.
But it is thought Underhill, who left Deutsche Bank's London office in March 2004, will take over the global role from interim senior vice-president of corporate communications Kiki Steimer. Underhill could not be reached for comment.
Steimer, who also holds the title of management support V-P, has been covering the global comms role since Christians' departure.
The company is fourth in grocery retailing to Wal-Mart, Carrefour and Tesco.
Underhill will join Ahold as the group faces price wars in many of its key markets and prepares to lock horns with investors, who are suing the company over its 2003 accounting scandal.
Shareholders brought the case over Ahold's admission that year that it had overstated earnings at its US Foodservices catering supplies unit by more than £493m. Ahold said on Tuesday this week that the case was scheduled to be heard in 2007.
Having joining Ahold in 2002, Christians had played an important role in rebuilding the company's reputation after the scandal broke the following year.
The company posted a net profit of £89m for the first quarter of this year, just shy of the £99m market expectation median but above lower expectations of £72m.