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.
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.