The 21-year-old rose through the academy ranks at the KC Stadium and made his first-team debut in August 2011, one of only two appearances for the Tigers to date.
East enjoyed more regular first-team involvement over the first half of this season having joined League Two side Northampton on loan, making 17 starts and also coming off the bench twice.
However, the last of those came at the start of December and he returned to Humberside in January.
Manager Martin Allen told Gillingham's official website: "He can play in both full-back positions, he can play in midfield and we are a bit short at the moment without (Andy) Frampton and (Charlie) Allen.
"We needed cover in both our full-back positions just in case - we have four games in 10 days so he will go straight into our squad which helps us because I think we are a bit short on numbers at the moment.
"I saw him play for Northampton earlier in the season and it was a Tuesday night when they played Wolves. He played full-back and I circled him on my sheet of paper - he's aggressive, athletic, hungry, has a good attitude.
"He's a character, a winner, he's tenacious, bombs forward, he's a good athlete and he will be good for us."