Huddlestone moves to the KC Stadium on a three-year deal for an undisclosed fee while Livermore joins on a season-long loan.
The 26-year-old moved to White Hart Lane in 2005 from Derby County and went on to score 15 times in 188 appearances.
Huddlestone has four caps for England, having made his international bow against Brazil in November 2009.
Livermore came through the youth system at White Hart Lane, breaking into the first team under Harry Redknapp in the 2011-12 campaign.
After making 38 appearances in all competitions, he made his England debut against Italy in August 2012, but found himself used less by Andre Villas-Boas and he now embarks on the seventh loan spell of his career.
The pair join Yannick Sagbo, Danny Graham, Allan McGregor, Steve Harper, Ahmed Elmohamady, Curtis Davies, Maynor Figueroa and George Boyd in moving to the KC Stadium this close-season.
Both players are set to take part in first-team training on Thursday, ahead of Hull's Premier League opener against Chelsea on Sunday.
