Bukayo Saka scored the decisive first-half goal in a tight semi-final second leg, sealing a 2-1 aggregate victory after the sides had drawn 1-1 in Madrid.
The Gunners capitalised on a vibrant home atmosphere to reach their first Champions League final in 20 years and their first European final since 2019.
“I saw a champions’ team today,” Seedorf told Amazon Prime.
“From the beginning to the end. They were in control, didn’t force the game in the first half and had to work a bit harder in the second.
“You don’t want to risk any more. They know how to defend. Gabriel was impressive today.
“We were worried (before), but the whole team were calm and composed. They gave it (all) until the very last minute.”
They will now face either Bayern Munich or reigning champions Paris Saint-Germain in Budapest at the Puskas Arena later this month.