Zoellick has not yet been replaced and concerns had grown that the department's top ranks were thinly staffed.
Rice is said to have approached several candidates, for what is widely regarded as a prestigious post, but without success.
Negroponte, 67, is stepping down as George Bush, the US president, develops a new strategy on Iraq.
Negroponte has held a series of challenging positions in the Bush administration and has been at the centre of the Iraq debate since before the US-led invasion in March 2003.
Negroponte served as US ambassador to the UN from 2001 to 2004 and ambassador to Baghdad until March 2005 before becoming intelligence chief.
The British-born son of a Greek shipping magnate, he also was ambassador to Mexico from 1989 to 1993.
He drew criticism from a number of Democrats during his time as ambassador to Honduras during Ronald Reagan's administration.
Critics said he turned a blind eye to human rights abuses when the country served as a staging point for the US-backed Contra war against Nicaragua's Sandinista government.
The Democrats, who take control of Congress on Thursday, have promised greater oversight of government agencies.
The Senate intelligence committee, for instance, is planning hearings this month on the intelligence overhaul that Negroponte helped put in place.
Negroponte's transition to the state department must be confirmed by the Senate, as would Bush's choice for his replacement.
Both changes will also create new openings for the Democrats to debate the administration's intelligence and foreign policy direction.
It is not clear who will fill Negroponte's position.
The job of his number two has been vacant since Michael Hayden, a US general, became CIA director in May.
Negroponte's likely successor is Mike McConnell, a retired admiral and director of the national security agency from 1992 to 1996.