The team, featuring Scotland's Commonwealth Games hopes Daniel Keatings and Dan Purvis along with Sam Oldham, Kristian Thomas and Max Whitlock, ended with a combined total of 265.953 points to finish behind Russia (267.959), while the Ukraine claimed bronze.
Britain had won gold in Montpellier in 2012, but this year was the first chance they had to defend the team title as last year's competition only consisted of individual elements.
With three of the five strong team competing on each apparatus and every score counting to the team total, the British boys commited no major errors in their routines, only a few small faults at the beginning of the competition on the rings costing them the chance to retain their title.
Whitlock was unable to control his landing and stumbled backwards for a score of 13.666, and Purvis took a few steps on landing his dismount scoring 14.333, while Thomas did not stick his landing on the vault to score 13.966.
However, they fought back superbly on the floor and pommel horse to secure the silver.
Thomas said: "We left ourselves a bit too much to do with a few early mistakes, but our character was fantastic.
"We are a very tight group and we all worked hard for each other and are really happy to have fought so hard and won the silver."
Whitlock produced the standout moment of the competition ahead of today's individual apparatus finals after he scored a hugely impressive 16.200 on the pommel horse in the final rotation, with a highly difficult routine, going up into a handstand midway through his performance.
There was plenty of support in the wings. Purvis started off with a clean, well-performed routine for 13.933, setting up nicely for Keatings to exceed that display with an excellent score of 15.008.
Earlier, Keatings had topped the scoring on parallel bars with 15.200 with a routine packed with difficult skills, while Oldham and Thomas both impressed on the high bar.
On the floor, Purvis, knowing the British boys needed to push on, executed his routing superbly for a great score of 15.200. Thomas followed up in similar fashion, his tumbles full of power with well-controlled landings to score 15.000. Last up came Whitlock and his routine was packed with twisting tumble runs and his trademark flair work on the floor, scoring a brilliant 15.700.
The silver medal continues a fine week for the men's team who claimed junior team gold and junior all-around gold and bronze ahead of today's apparatus finals when Whitlock will return for the pommel horse and will be joined on the floor - an event he won at last year's individual European Championships - by Purvis.
Thomas and Oldham will contest the high-bar final.