Authorities said Potts' cell phone activity conflicted with his alibi, and witnesses contradicted his story about where he was when Franklin vanished.
Before she disappeared, Franklin had complained to police that Potts had telephoned her making threats.
"She was in the process of obtaining an order of protection when she ended up missing," police Cmdr. Steve Peterson said. "When it leads to this, it's tragic for everybody."
Franklin's disappearance triggered a frantic search. Family members and volunteers papered the city with fliers, took out a newspaper ad seeking the public's help and launched a Web site.
Her nude, decomposing body was found Sept. 27, eight days after she was reported missing when she didn't show up for a work meeting. She was a pharmaceutical sales representative for Indianapolis-based Eli Lilly.
Days before her body was discovered, her car and some personal items were found near an abandoned building in Hammond, Ind., about 20 miles from Chicago.
Potts is being held at Cook County Jail and is scheduled for a bond hearing Monday. It was not immediately clear whether he has an attorney. He has denied any involvement in Franklin's death.
"What would be the motive for me to do anything to her?" Potts told the Chicago Tribune last month in an interview the newspaper did not publish until Saturday. "It's an unfortunate situation, but it doesn't mean I should be run through the ringer. I had nothing to do with it."
Potts has a criminal record and a history of violent threats, mostly against women, the newspaper reported.
Police declined to give details on Potts' alibi.
The Cook County medical examiner's office has not released Franklin's cause of death, a spokeswoman said Saturday. She was identified using dental records.
