Laugher, from Ripon, almost missed out on a place in the final after an error-strewn display in the semi-finals.
But the 21-year-old produced a flawless performance throughout the final at the Maria Lenk Aquatics Centre and totalled 523.85 points over the six rounds.
China's Cao Yuan was a dominant force at the top of the leaderboard and won gold by 24 points on 547.60.
Yuan only dropped under the coveted 90-point mark twice in the competition, while Laugher had three dives over the mark.
Germany's Patrick Hausding took the final place on the 498.90.
Laugher's silver adds to the gold he won alongside Chris Mears in the 3m synchronised event last Wednesday and makes him Britain's most succesful diver in history.
Harrogate-born diver Oliver Dingley was a surprise package in the early stage but dropped down to eighth-place on 442.90.
Dingley was competing in his first Olympic final for adopted nation Ireland, whom he qualifies through his grandmother.
Both Dingley and Laugher dived together as juniors in Harrogate before the former moved to Plymouth.
Laugher crashed out of in the 3m springboard event four years ago in London when he slipped off the board in qualification.
Once again, the City of Leeds diving club member struggled in the opening rounds and only qualified for the final in 12th place out of 12 qualifiers.
That meant he was forced to dive first in the final but he set an early marker with scores of 81.60, 91.00 and 90.10 in the final.
A 76.05 in the four round was his worst dive of six but he recovered with his best in round five to nail a 3.8 degree of difficulty forward four and a half somersaults and 96.90 points came his way.
That meant he needed just 60 points in the final round to bag a medal and he scored 88.20 to put the silver beyond Patrick Hausding.
China's Yuan held off the Brit, however, and won gold with a perfect final dive, scoring 96.90.
Laugher told BBC Sport: "It's been a mixed experience.
"My prelim was a bit nervy and the semi was even worse - my worst in three years. But to come away and turn it around, I'm really pleased."