By Jeff Zeleny, Dan Merica and Arlette Saenz, CNN

(CNN) -- Joe Biden has selected his running mate, revealing to top advisers on Tuesday the woman he will invite to join his Democratic presidential ticket, two people familiar with the matter tell CNN.

He is poised to make the announcement as early as Tuesday.

The former vice president had spoken directly to the final contenders, according to people familiar with the process, through either face-to-face meetings or remote conversations. Officials would not say which of the candidates visited Biden in person, but CNN confirmed last week that Michigan Gov. Gretchen Whitmer had flown to Delaware for a meeting. California Sen. Kamala Harris and former Obama national security adviser Susan Rice are among the others seen as the most serious contenders.

CNN had previously reported that Biden is also believed to be considering California Rep. Karen Bass, chairwoman of the Congressional Black Caucus, Sen. Elizabeth Warren of Massachusetts and Sen. Tammy Duckworth of Illinois, people familiar with the search say.

In yet another sign that the pick is imminent, a Biden campaign official told CNN on Tuesday that they have assembled the staff for Biden's future running mate.

Karine Jean-Pierre, who joined the Biden campaign as a senior adviser in May, will lead the running mate's team as chief of staff. Jean-Pierre had previously worked for Barack Obama and Martin O'Malley's presidential campaigns.

Two veterans of the Obama-Biden administration are also joining the team. Liz Allen, who served as deputy communications director for Biden as vice president as well as deputy communications director in the White House, is joining as communications director to the running mate. And Sheila Nix, who was chief of staff to Biden's reelection campaign in 2012 and served as Jill Biden's chief of staff in the White House, will be a senior adviser to the running mate and spouse. The vice presidential pick is expected to also add a few of her own advisers to the team.

Whoever Biden settles on will be a history-making choice in her own right, becoming only the third woman to be nominated as a vice presidential candidate for a major party's ticket.

This is a breaking news story and will be updated.