Coleman was stopped by Delaware State Police on I-95 on Thursday afternoon after an all points bulletin for his vehicle was put out by Rhode Island. Correia's family said her body was found in the trunk of his vehicle.
Court paperwork shows troopers took Coleman into custody on charges of being a fugitive from Rhode Island where he was wanted for kidnapping, refusal to report death with intent to conceal a crime and mutilation of a dead human body.
All three crimes are felonies in Rhode Island.
Delaware officials say Coleman's extradition is "imminent."
Providence police said Thursday that Coleman was not known to police and he had no criminal record in Rhode Island.
The FBI says it is assisting Boston police in the investigation.
Suffolk County District Attorney Rachael Rollins and Boston Police Commissioner William Gross held a news conference Friday afternoon at which they described the multistate, multijurisdictional case as "very complicated and complex."
Raytheon, Coleman's employer, said, "We defer any further inquiries to law enforcement. We are cooperating fully with the investigation."
Johnson and Wales University, which has buildings throughout Providence and said it is reviewing security cameras from their buildings near Coleman's Chestnut Street address.
The Correia family says a GoFundMe page has been set up to take care of Jassy Correia's 2-year-old daughter and pay for her future education.