City completed the treble of Champions League, Premier League and FA Cup titles, matching Manchester United's feat in 1999 and drawing comparisons with Guardiola's 2008-09 Barcelona team.
The two teams have met eight times in the European Cup, with Real winning four times and Liverpool three.
Ancelotti replaces Zinedine Zidane, who left Real last month.
"...This club is built on what they did. It's built ... on (Bill) Shankly, (Bob) Paisley and (Joe) Fagan and all the others, but on these players... Steven Gerrard -- this club's built on, in the last 20 years, on Stevie's legs..."
Seven different managers have tried and failed to recapture Liverpool's long-lost domestic glory before Klopp arrived at Anfield in 2015 to -- in his own words -- turn the Merseyside club from "doubters into believers".
The reigning champions have won 53 and drawn 11 of those 64 games, scoring 169 goals and conceding 42 for a total of 170 points.
Real Madrid coach Zinedine Zidane is leaving the European champions after two years in charge.
Real Madrid coach Carlo Ancelotti is counting on his wealth of experience to help fix the holders' midfield woes as they prepare to host FC Basel in Tuesday's Champions League Group B opener at the Bernabeu.