The 21-year-old attacking midfielder has signed for an undisclosed fee, reported to be around £8.5m with Real Madrid retaining a 30% sell-on clause, on a contract until June 2031 with a club option to extend by a further year. He will wear the number eight shirt.
Speaking to FFCtv, Palacios said: "I am very emotional to be here. I believe it is the perfect step in my career. The club is showing a lot of trust in me, and I'm going to show it on the pitch."
Fulham owner Tony Khan added: "I'm excited to welcome César Palacios to Fulham! César is a hard-working and creative young midfielder, and we believe that he will be a good addition to our squad under Álvaro's leadership.
"This is an important day, as we have signed two exceptional young talents to the team, whom we believe will both be part of a bright future for the club! Come on Fulham!"
Palacios's arrival follows Fulham's separate deal to sign forward Gonzalo García from Real Madrid in a package reported to be worth close to £35m, with new head coach Arbeloa driving both moves.
Palacios grew up in Numancia's youth system before Real Madrid signed him six years ago, and he spent the 2023-24 season progressing into the Castilla set-up.
He thrived once his future Fulham boss took charge of the reserve side, contributing 19 goals or assists (15 goals, four helped) across 32 games for Castilla under Arbeloa, form that earned him a first-team debut the moment Arbeloa was promoted to the senior job. He went on to make seven Real Madrid appearances in total last season, two of them in the Champions League.
Spain have used him at Under-20 level, and he scored seven times in a dozen outings for the Under-19s, underlining the goal threat Fulham are banking on from midfield.