Weir, a highly-rated midfielder, joined Bristol during the mid-season break in 2015 but could not prevent the Vixens from being relegated from WSL 1.
The 20-year-old previously lifted the FA Women's Cup with Arsenal in 2014.
"Liverpool Ladies are a really ambitious club and I am confident that we can win more trophies over the next few seasons," told the club website.
"It is a great move for me. There are so many talented players here and I am really looking forward to playing alongside them in order to develop my game."
Liverpool Ladies have completed the signing of Scotland international Caroline Weir from Bristol City Women.