The side will kick things off at home on 30 September against reigning champions Anadolu Efes.
Laso's charges, winners of the last three trophies, will try to defend the title from 11 to 12 September in Tenerife.
The US point guard averaged 17 points and 5.2 assists with Lokomotiv Kuban in the EuroCup.
"When you sign for a club like this, you've only got one objective in mind: to win", said the madridista recruit.
The French power forward joins from Asvel where he averaged 11 points and 4.2 rebounds in the last Euroleague.
"I can't wait to get started playing with the team and in front of the fans", said the French power forward.
The French point guard comes to the club from Asvel Villeurbanne, who won the league and cup this season.
“I'm a player who gives it his all on court and it's always been a goal of mine to work with Laso”, said the new Real Madrid point guard.
Rudy, Abalde and Garuba all played in Spain's 83-76 defeat against the USA. (83-76).
“I’m eager to keep helping the team and to fight for all the trophies”, said the Madrid player.
The coach will stay at the club for two more seasons, where he has won 2 Euroleagues, 1 Intercontinental Cup, 5 Leagues, 6 Copa del Rey and 6 Supercups.
Real Madrid beat Barcelona in over-time in the final in Valencia to get their hands on the title for the third time.
The Madrid coach receives the award from the Spanish Basketball Coaches Association (AEEB) for the fifth time in his career.
The madridista center collected the awards at the WiZink Center in the build-up to the first game against Herbalife Gran Canaria.
The madridista center has won the Rising Star Trophy, a prize handed to the competition's best player under 22 years old.
Real Madrid is the most decorated club in the history of this competition.
Taça dos Campeões Euroliga de Baskequetbol
10
Ligas
35
Taça do Rei de Basquetebol
28
Supertaça de Basquetebol
7
Taça Intercontinental de Basquetebol
4
Campeonato do Mundo de Clubes
1
Taça das Taças Basquetebol
4
Taça Korac
1
Taça ULEB Basquetebol
1
Taça Latina de Basquetebol
1
Torneio de Natal
25
