Gibbons, who battled back to make the London 2012 squad following six months out after shoulder surgery, battled through to the semi-finals and then defeated world champion Audrey Tcheumeo with an ippon throw in golden score.
However, the gold proved just out of reach for the 25-year-old, who was watched by Prime Minister David Cameron and Russian president Vladimir Putin, a judo black belt.
Fourth-seeded American Kayla Harrison claimed a narrow victory by two Yukos, which was the United States' first ever women's judo Olympic title.
Gibbons was coached by Kate Howey, the last British judo fighter to win Olympic silver at the Sydney Games.
"As a kid growing up, Kate was my hero. She has been a big part of my preparation for this and I hope I can inspire young children how she inspired me," said Gibbons, raised just a few miles away in Greenwich.
"Hopefully lots of people have had the chance to view judo over this Olympic period and that they want to get involved and their kids want to get involved.
"It is great I was able to do this because our team have all been capable of it, but have had a pretty bad time over the past few Olympics and hopefully this proves we can do it at this level."
Today will see the final heavyweight judoka in action, with veteran Karina Bryant leading Team GB's hopes while French colossus Teddy Riner goes for gold in the men's over-100kgs.