USAF Academy via AP

The U.S. Air Force has identified Capt. Lucas Gruenther, seen here in 2003, as the pilot of an F-16 fighter jet that went missing Monday on a training mission over the Adriatic Sea.

The body of a U.S. Air Force pilot whose F-16 fighter jet went missing Monday after it took off for a training exercise from Aviano Air Base, Italy, has been found in the Adriatic Sea.

According to a statement released by the family, the body of Capt. Lucas Gruenther, 32, was found Thursday afternoon.

"A compassionate husband, a loving son, and a devoted brother; Luc leaves behind a family who loves him dearly and a legacy of achievement," the statement reads. "We will never fully recover from our loss, but take heart in the knowledge that during his all-too-short time in this world, he made a significant difference in the lives of all whom he met."

The Air Force also issued a statement, offering condolences to the family.

"Captain Gruenther was an outstanding officer who epitomized what it means to be an Airman," said Brig. Gen. Scott J. Zobrist, 31st FW commander. "He was not only a first-rate pilot; he was an exceptional leader whose presence will be sorely missed."

The statement said Gruenther, an Air Force Academy graduate, had flown numerous combat sorties during a six month deployment to Afghanistan in 2011, and that a board of officers will investigate the incident.

Earlier in the week, fragments of carbon steel and other debris were found floating in the northern Adriatic. At the time, the Air Force said it believed the debris belonged to the wreckage of the missing aircraft and continued its search-and-rescue operation.

The family kept its hopes up, and in a blog post published on the base's website, his wife, Cassy, wrote: "If anyone could survive something like this, it would be Luc."

Officials then confirmed that Gruenther's drogue parachute and his helmet were among the debris found in the water. Cassy wrote that they remained optimistic, as they were told the helmet was found in good shape.

"That's why I know he's coming home," Cassy wrote in the blog post. "If he has his mind set on something, he will find a way to make it happen. He'll find a way; whatever he has to do."

NBC Bay Area said Gruenther was from Twaine Harte, Calif. He married his high school sweetheart, who is expecting the couple’s first child, Serene, in a few weeks.

The Gruenther family thanked "the many people who volunteered their time and resources to help bring Luc home." The search operation included aircraft and ships from the United States and Italy.

NBC New staff writer Kari Huus contributed to this report.