The doubles will be played Saturday and reverse singles are Sunday in Belgrade.
Djokovic hopes to recover from the jet leg after losing the U.S. Open final to Rafael Nadal on Monday.
"I arrived yesterday, but it's not the first time that I have one or two days to get ready," said Djokovic, who lost in four sets in New York. "I know my body, and I hope I can prepare for the opening match."
Making things even more difficult for the 26-year-old Serb is the choice of an indoor clay court -- originally picked by the hosts to slow Raonic's booming serve. Djokovic will have to adjust to the change in surfaces in the middle of the hard-court season.
"It's obvious that I'm tired, time zones, jet leg, plus adjustment to the clay, but I feel fine and have a lot of motivation playing for my country," Djokovic said.
The 23-year-old Pospisil, ranked 41st, has never played Djokovic before.
Canada has never made it this far in the Davis Cup, while Serbia won the event in 2010.
Raonic said Serbia is the favorite, "but that doesn't mean we don't have our chances."
The towering Canadian has climbed in the rankings and is currently 11th.
"I'm now playing better on clay, and I feel very confident now on the surface," Raonic said.
Tipsarevic, once a top-10 player who has recently dropped in the rankings to 23rd after a string of injuries, is 0-3 against Raonic.
The winner will face either the Czech Republic of Argentina in the final in November.