The lock replaces prop Mike Shelley at the helm, having returned to the Tykes line-up three weeks ago, after recovering from a serious knee injury.
He will take charge for the first time in Friday's Heineken Cup match away to pool leaders Edinburgh.
'I thought that further down the line I might get to captain Leeds, but never so early in my career. It is a great honour,' the 24-year-old said.
Palmer is pushing for a place in the England squad having made his debut against the USA in 2001 - his sole appearance to date.
He will work in tandem with vice-captain Dan Hyde and intends to lean on the experience of Shelley, who has been made club captain.
But rugby director Phil Davies has no doubt the decision is in the best interests of the club.
'Tom has all the potential to be a great captain for the Tykes for many years to come,' said Davies.
'Mike has done a fantastic job over the past couple of years and has steered us through to the current point.
'But I am keen to get the most from Mike as a player over the coming years and I feel the time is right for Tom to take up the reins.
'I have always thought of Tom as a potential captain for the club - and with us now having a young core to our squad, I hope he will be able to lead this group of players to the next level,' he added.