In a way, the title says it all.
Rumors are bite-sized backstory.
Every rumor you hand out in your campaign is a bit of common knowledge. It conveys some information about the world around the PCs. They'll build up over time, and feed into each other. The player's musings on the rumors will inspire actions and new rumors, which will in turn connect to things they already know from actual play.
If you combine this with letting the players make stuff up, your backstory will come to life organically and have immediate buy-in from the players.
Another tip? The best rumors are actionable.
One big problem is backstory is no one wants to hear it. But everyone likes to hear rumors, if they're actionable. You've broken up the backstory of the world into bite-sized pieces tied to potentially useful and rewarding information.
Okay rumor: Prices are up because of bandit raids.
Better rumor: Prices are up because of bandit raids, led by the bandit chief Sherven of Grey Woods.
Great rumor: Prices are up because bandits are raiding the northern road under the command of Sherven of Grey Woods - and the local merchants are pulling together a reward for his head!
The first tells you information. The second, more information. The third? It's a plot hook and information. The next bandit the PCs meet, or merchant they talk to, Sherven of Grey Woods is coming up in conversation. So is the size of the reward.
This is also why I don't determine truth or falsehood. I'm just building a shared story about the world. I'm not really sure for some rumors if they are true or not. Some I'm sure are totally false. Others, absolute fact in all particulars. Most, though, fall in between. They may turn out to be true, they may turn out to be false, and they may be misinterpreted - which affects their effective truth.
Doling out a big wad of backstory is not fun for the players, but doling out rumors works well. Just realize you're building the backstory of the world as you do.