American Ward will defend his WBO belt and the WBA and IBF light-heavyweight titles that he won against the Russian last November.
The 33-year-old beat Kovalev, 34, by a unanimous decision but was floored in the second round of the fight.
Ward said: "I am looking forward to making a statement in this fight."
Despite all three judges scoring it 114-113 to Ward in the first fight, Kovalev was unhappy with the decision.
Ward, who extended his record to 31 wins from 15 bouts, does not think his victory was controversial.
"Some of you think I lost the fight, but you've got to look at the other side of that coin. There are a lot of people who are convinced I won it," he said.
The build-up to the rematch has been heated, with Kovalev storming out of Thursday's press conference.
The 'Krusher' pointed at his opponent and said "be prepared", then left before an obligatory face to face.
He has also previously mocked Ward's 'Son of God' nickname, referring to him as the 'Son of Judges' instead.
Kovalev's record stands at 30 wins, one loss and one draw, with 26 of his wins coming via knockout.
The pair weighed in at 12st 5lbs on Friday, two pounds under the light-heavyweight limit.
Andre Ward beat Britain's former world champion Carl Froch in a convincing points win in December 2011.
He has also beaten Liverpool super-middleweight Paul Smith, stopping him in the ninth round in June 2015.
Smith, 34, is also in action on Saturday as he faces WBA 'regular' super-middleweight world champion Tyron Zeuge in Hessen, Germany.
His 25-year-old opponent is the only current world champion from Germany.
It will be Smith's third shot at winning a world title. His previous two attempts were also against a home favourite in Germany, when he lost back-to-back fights to Arthur Abraham in September 2014 and February 2015.
Smith's trainer Joe Gallagher has described Saturday's fight as the "last roll of the dice" for his fighter.

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Cheshire, 21, who has missed much of the past three years because of repeated concussions, finished sixth.
"I'm really happy with my progression, but I just couldn't put it down tonight," she told BBC Sport.
"It happens and I'm going to take positives from being out there against the best in the world."
Japan's Ayana Onozuka (89.80) took gold in Sierra Nevada ahead of France's Marie Martinod (87.00) and American Devin Logan (84.20).
Cheshire was regarded as a potential medallist at the Sochi Winter Olympics, but a heavy crash in training resulted in a serious concussion that meant she missed the event.
She suffered two further concussions and experienced panic attacks over the next 18 months, only returning to full-time competition this season with under a year to go to the Pyeongchang Games.
"I'm over all of my head injuries," she said. "I'm in a really good place, feeling super-confident and enjoying it more than ever."
Earlier on Saturday, James Woods and Izzy Atkin qualified for their respective slopestyle finals, which will take place on Sunday.
Woods, who finished fifth in Sochi, scored 86.00 to finish fourth in his heat while Atkin, who won GB's first ski slopestyle World Cup gold medal earlier this month qualified in third place.
Although GB's Tyler Harding, Cal Sanderson and Michael Rowlands all missed out, organisers subsequently revised their rules and have added a semi-final on Sunday with the top four to qualify for an extended 16-strong final.
Two-weight world champion Andre Ward says he will remove "any doubt that may be out there" in his Las Vegas rematch with Sergey Kovalev on Saturday.
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British halfpipe skier Rowan Cheshire crashed in all three of her final runs, but still secured Britain's best-ever World Championship result in the event.