Moving Gonzalez to center field had been a strong possibility ever since the Rockies traded Fowler to Houston over the winter. Weiss revealed the decision Saturday.
"We are feeling comfortable with the alternatives, watching these guys run around," Weiss said, according to MLB.com. "The big thing is we want to keep [Gonzalez] on the field.
"Risk and reward has kind of swung the other way. We are in a different place than we were in the fall. That's what it comes down to."
Gonzalez, a three-time Gold Glove winner, said he'd be fine with a move to center field so long as he didn't bounce back and forth as he had earlier in his career. He said that affected him both physically and mentally.
The Rockies, coming off an injury-riddled 74-88 season, need Gonzalez to remain healthy in 2014.
In 2010, the Venezuela native hit .336 to win the National League batting title and was third in the MVP voting. It earned him a seven-year, $80.5 million contract.
But the 28-year-old hasn't played more than 135 games in any season since.
Gonzalez had 26 home runs on July 20, but didn't hit another the rest of the way because of the troublesome finger injury that led to a lengthy stint on the disabled list.
Gonzalez decided against offseason surgery, but has moved his right hand up on the bat in hopes he won't aggravate it.
The Associated Press contributed to this report.