Serrano's arrival addresses a position Bordalas flagged as a priority following the departures of Mauro Arambarri and Luis Milla, with Javi Munoz and Neyou also possible exits after being left out of matchday squads throughout pre-season.
Getafe will compete in the Conference League this season, adding a new dimension to Serrano's first campaign away from his home city.
The Zaragoza-born midfielder made his professional debut for the Aragonese club and went on to captain the side, featuring in 200 official matches and contributing 13 goals and 12 assists across his career there.
He also won two caps for Spain's Under-21s, against Lithuania and Russia in 2021. Real Zaragoza confirmed the club received no financial compensation for his departure.
Serrano marked his exit with an emotional video message to Zaragoza supporters.
"Dear Zaragocistas, the moment I never imagined would come has arrived: saying goodbye to the club of my life," he said.
"It's been a very difficult decision. I never thought about wearing another badge because Zaragoza was always much more than a club to me. That's why today I just want to say thank you.
"Thank you to all the coaches, team-mates and staff who have been with me since I arrived as a boy, growing up with this badge and helping me become who I am today."
He continued: "And thank you above all to you, Zaragocistas, for your affection, your support and for always being there, even in the most difficult moments. I hope I'm remembered as someone who always gave everything for Zaragoza. I leave with pride at having fulfilled the dream I had since I was a child: to be captain of Real Zaragoza's first team.
"But this doesn't change what matters most. I will always be a Zaragocista. La Romareda will always be my home. This isn't goodbye, it's see you later. I love you, Zaragocistas, now and always. Come on Real Zaragoza."
His departure has not been well received by sections of the Zaragoza support, who feel the club's new majority shareholders have done little to change what they view as erratic sporting decision-making, given that figures from the previous ownership, including Jorge Mas and Juan Forcen, remain involved at the club. Zaragoza were relegated to the third tier last season.