He told the club's official website: "With the recent results I'm not expecting to walk straight into the starting line-up, but I've always been taught to fight for my place and that's what I'll be looking to do.
"Being out of contract [in the summer] and not playing, people tend to forget about you, so it's obviously a challenge for me to come down here and try to prove myself.
"It's going to be a good challenge for me to try and pick up some games, and hopefully we'll see what we can sort out at the end of the season, if I do well enough."
Hendrie revealed that Brighton's attractive style of football had lured him to the club. He added: "There are lots of teams in League One that like to play the ball long, but I want to get the ball down and play football, so that's my main reason for coming here."