Randal Gebo, 61, of Barre, was arrested Wednesday during a traffic stop in Downers Grove, Illinois, said Vermont State Police.
Police say they traced Gebo's travels from Vermont to Arkansas, as he used Cook's debit card to withdraw cash and buy gasoline, and video surveillance showed Gebo driving Cook's vehicle.
Police in Vermont are seeking the public's help as they continue to investigate the death of a Barre woman and search for her boyfriend.
Gebo was arrested without incident on outstanding Vermont arrest warrants for aggravated vehicle operation without owners consent and fraudulent use and possession of a credit card issued to another.
Cook remained in IL on July 19 for an appearance in federal court, according to a Vermont State Police spokesman. Cook was Gebo's girlfriend, according to media reports.
The last time anyone had been in contact with Cook was July 3, when she spoke to a relative on the phone, according to state police.
State police wants to talk to anyone who may have visited the Shady Rill picnic area near the Wrightsville Reservoir in Middlesex between July 3 and July 6. Anyone with information is asked to call Vermont State Police at 802-229-9191. An autopsy revealed she'd been killed, but the method was not disclosed.