Reports have suggested that it is a four-year deal until 2029 but the club's website has only described the contract as "long-term".
The 21-year-old Northern Irishman is likely to get more first-team opportunities after fellow right-back Trent Alexander-Arnold confirmed that he was leaving Anfield earlier this month.
However, Bradley will have competition if Liverpool successfully trigger the release clause of Bayer Leverkusen's Dutch right-back.
"You've just got to keep your head down and keep working hard.
"It has been a fantastic two years [with the senior team].
He made five Liverpool appearances in 2021-22 before joining League One Bolton Wanderers on loan for 22-23, where he was named their player of the year.
He returned to Anfield in 2023 and played 23 times across all competitions, and has made 27 appearances in 2024-25.
Bradley has also scored four goals in 24 international appearances for Northern Ireland.
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