Morton played at Premier League and Champions League level with the Anfield club and spent last season on loan at Championship club Blackburn Rovers.
Head coach Liam Rosenior said: "For us to capture a player of Tyler’s pedigree and potential, again fighting off a lot of competition, I’m absolutely over the moon.
"He played at a high level last season in a team in Blackburn that just missed out on the play-offs. He’s played in the Champions League, Premier League and in cup games for a top club in Liverpool.
"The fact Liverpool and Tyler believe Hull City is the best place for him to continue his development says a lot about the direction we’re moving in as a football club.
"Tyler has everything I like in a midfield player. He’s brave and has got unbelievable technical quality, which is important for the way we play. He can see a pass, has a great football brain, understands the game with his defensive positioning and is aggressive."
Earlier in the night, City completed the signing of Furlong.
The 21-year-old, who signed a new deal at Albion in the summer, has joined the Tigers on a permanent deal and provided another defensive option on the left alongside Ruben Vinagre.
He has signed a three-year deal with a further year’s option.
Furlong joined Brighton’s academy in 2019 from Irish club Shamrock Rovers and he made his first-team debut last August.
He spent a loan spell at Scottish Premiership club Motherwell in the second half of last season and made 16 appearances. Brighton turned down a bid from Legia Warsaw earlier this summer.
Earlier on deadline day, homegrown product Brandon Fleming joined Shrewsbury Town on loan for the rest of the season and Xavier Simons linked up with another League One side in Fleetwood in an indentical arrangement.