The sun was shining as the Reds touched down in Moscow at 8pm local time on Monday evening after a four-hour flight from Manchester.
Sir Alex and his 24-man squad headed straight to the team hotel via a police escort for some dinner, before retiring to their rooms to rest.
On Tuesday, both United and Chelsea will get their first look at the Luzhniki Stadium during late afternoon training sessions in what are expected to be somewhat humid conditions.
Sir Alex and Avram Grant will also face the press ahead of Wednesday's Champions League final which will be officiated by Slovakian Lubos Michel.
He was the man who took charge of the semi-final between Chelsea and Liverpool in 2005, when Luis Garcia was controversially awarded the goal that sent Liverpool through to the final.
Michel will be backed by assistant referees Roman Slysko and Martin Balko, with Vladimir Hrinak performing fourth official duties.