"Markus Paul, surrounded by his family, passed away at the hospital this evening at the age of 54," the Cowboys said ... "The cause of death is pending."

Team owner Jerry Jones issued a statement, saying, "The loss of a family member is a tragedy, and Markus Paul was a loved and valued member of our family."

"He was a pleasant and calming influence in our strength room and throughout The Star."

"His passion for his work and his enthusiasm for life earned him great respect and admiration from all of our players and the entire organization."

"Our hearts are broken for his family and all of the individuals whose lives he touched and made better."

As we previously reported, Paul suffered a medical emergency at Cowboys headquarters at around 7:30 AM Tuesday morning and was transported to a nearby hospital.

Doctors scrambled to save Paul -- but despite their best efforts, he passed away Wednesday evening.

Paul had been a mainstay in NFL locker rooms for decades ... he played for the Chicago Bears from 1989 to 1993 and had a stint with the Tampa Bay Buccaneers in '93 as well.

He later went on to become an assistant strength and conditioning coach for the New Orleans Saints in 1998. From there, he worked for the Patriots, Jets, Giants and Cowboys ... winning FIVE Super Bowls with those teams.

The Cowboys had just promoted him to lead their lead strength and conditioning department in January.

"Markus was a great coach and one of the best guys that I have ever known," NY Giants legend Eli Manning said on Twitter this week. "He will be missed."

Former Giants kicker Lawrence Tynes added, "My heart is heavy. One of the finest men and coaches I have ever met. The world lost a GREAT MAN today. We love you! RIP Markus Paul."