Cole was placed on the 15-day disabled list Monday and traveled to Los Angeles for a second opinion with a specialist, who confirmed posterior elbow inflammation.
"This is very encouraging news," Pirates trainer Todd Tomczyk said. "He is now focused on how he is going to help this team win some ballgames the rest of the season."
"It's comforting to have confirmation that you'll be OK," Cole said.
Cole is on the DL retroactive to last Thursday, meaning he is eligible to return Sept. 9.
Cole had a 6.08 ERA in five August starts and said he alerted the team of a "level of discomfort that was concerning" after allowing five runs and seven hits in five innings last Wednesday against Houston.
Tomczyk said it's uncertain how Cole was injured. He missed time in spring training with sore ribs and spent more than a month on the disabled list earlier this season with a strained right triceps.
"That is an ongoing discussion. He did have a slow start to the season with the rib injury," Tomczyk said. "That could be a factor. And there's the assumed risk of throwing a baseball."
Cole's absence means all five starters from the beginning of the season are no longer in Pittsburgh's rotation. Yet the Pirates remain in the thick of the playoff race, trailing St. Louis by two games for the second NL wild card.
"It's like coming back from a road trip and your wife has rearranged the furniture," manager Clint Hurdle said. "After you bump your shin a couple times, you've got to find a different way to cross the living room.
"We've had to find a different way to get across the room this year. And it's been a really good opportunity to learn."
Also on Tuesday, the Pirates recalled infielder Alen Hanson and selected left-hander Kelvin Marte from Triple-A Indianapolis.
To make room on the 40-man roster for Marte, left-hander Kyle Lobstein was designated for assignment.
This will be Hanson's second stint with the Pirates this season. He singled off Atlanta's Bud Norris for his first major league hit on May 17 before being optioned back to Indianapolis two days later.
In 110 Triple-A games this season, Hanson has batted .266 with 15 doubles, seven triples, eight home runs, 32 RBIs and 36 stolen bases.
The 28-year-old Marte has no major league experience. In 34 appearances with Indianapolis, Marte is 4-3 with two saves and a 3.67 ERA. He made his last three appearances as a starter, going 2-1 with a 1.69 ERA.
Information from The Associated Press was used in this report.