Media mogul Rupert Murdoch shut down News of the World in July after it was revealed that staffers had hacked into voicemails of public and private figures to get details about their lives.
Grant testified in London Monday as part of an inquiry into the newspaper's practices. Earlier, the parents of a murdered schoolgirl whose phone was targeted by the tabloid described how the hacking had given them false hope that their daughter was still alive.
Grant testified that he believes his phone was hacked by Britain's Mail on Sunday tabloid. This marks the first time he has implicated a newspaper not owned by Murdoch in the wrongdoing.
Grant said a 2007 story about his romantic life in the paper, owned by Murdoch rival Associated Newspapers Ltd., could only have been obtained through eavesdropping on his voicemails.
Over two and a half hours of testimony, Grant described years of tabloid pursuit that began after his breakthrough hit, "Four Weddings and a Funeral," in 1994.
Incidents included a mysterious break-in at his apartment during which nothing was stolen. Descriptions of the apartment later appeared in a tabloid newspaper.
Prime Minister David Cameron set up the inquiry into media ethics in response to an evolving scandal over phone hacking in Britain.
The inquiry, led by Judge Brian Leveson, plans to issue a report next year and could recommend major changes to the way the media in Britain are regulated.
The Associated Press contributed to this story
