Villa will pay 47.5 million pounds up front, with a further 17.5 million pounds available in add-ons.
Jackson arrives at Villa Park following Ollie Watkins' move to Saudi Pro League side Al Hilal, with the 25-year-old expected to lead the club's attack.
The move also gives Jackson the chance to reunite with Emery, who worked with him at Villarreal before the striker joined Chelsea in June 2023.
"Emery was a big factor when I arrived in Spain," Jackson said.
"He's been very important to me since the beginning; he's always asking about my family.
"He developed me in Villarreal, and I'm very happy to be here and working for him again."
Jackson said Emery's vision for Villa was a major reason behind his decision to return to the manager.
"With the coach, I've known him for a long time," he said. "With him calling me and from talking to him, he explained the project to me.
"I like the project so much, and that's why I'm here. Hopefully we can do a lot of things together."
Jackson scored 30 goals in 81 appearances for Chelsea before spending last season on loan at Bayern Munich, where he scored eight goals in 23 league games.
He has also established himself as an important member of the Senegal national team, winning 37 caps and scoring eight international goals.
The striker already knows several members of the Villa squad and believes the team can challenge for silverware.
"Hopefully we can win many games and trophies as well because that's what every player wants to do," Jackson said.
"I want to score a lot of goals for the team as well. Hopefully we can achieve that and win some trophies."
Jackson also outlined what he intends to bring to Emery's side.
"I will bring my spirit, fighting for the badge, fighting for the coach, as I always do," he said. "That's what I want to bring, and to score some goals as well.
"I'm very happy to be here."
After months of speculation over a possible move to Villa Park, Jackson was delighted to finally make the transfer happen.
"I'm very happy because it's a massive club," he said. "I've been looking forward to joining here for a few years.
"I'm very happy that I'm here finally. I'm ready to work."
Anthony Elanga and Yoane Wissa netted in the second half as Newcastle United inflicted a second consecutive Premier League defeat on Tottenham Hotspur with a 2-0 victory at the Tottenham Hotspur Stadium.
Liverpool's difficult Premier League run continued as Víctor Munoz scored his first goal for the club to earn a 2-2 draw against Nottingham Forest at Anfield.
Roberto De Zerbi has admitted he did not expect Tottenham Hotspur to have such an ambitious transfer window after the club backed him with more than three hundred million pounds in new signings.
Amit Bhatia said it would be a "huge privilege" to become part of Liverpool's future as the club prepares for a new minority investment.
