While the length of the deal is undisclosed, the Athletic reports it will run to 2029.
The 21 year-old told Liverpoolfc.com: "I think more than anything I'm just growing into my body a bit more now.
"I feel a lot more physically strong, I feel quicker, I feel more powerful – and I think that's really helping me when I do play games.
"I think there's massive improvement from this time last year, and hopefully I can keep going on that trajectory and just keep getting better.
"I just want to keep improving, keep getting better every day. I just want to try to maximise whatever my potential is and try to be the best version of myself. Hopefully I can do that in the years to come and just keep getting better."
Slot style suits me
On playing under manager Arne Slot, Bradley also said: "I've loved playing under it this season.
"It's been really good and I feel like it suits me really well, because I definitely feel like I've played better this season than I did last season.
"I feel like I'm improving under the new boss. It's been really good and hopefully it continues."