Rocket League's Tournaments mode, which will allow players to create and join bracketed, single elimination tournaments, will be available next week for a brief beta test. Starting on Wednesday, February 21 at 10 am PST, players can opt in to the Tournaments beta branch on Steam and test it out until Friday, February 23 at 5 pm PST.
After the start time, you can join by right clicking Rocket League in your Steam library, hitting 'Properties,' navigating to the 'Betas' tab, and selecting the 'Tournaments Beta' branch. Once you've done that, the beta client will replace your standard, live client. You won't lose any of your player data, and though you won't be able to play ranked in the beta, deselecting the beta branch will revert you to the live version at any time.
Tournaments will be officially added in the Spring Update, sometime in March or April. We also learned recently that the existing alternative modes like Hoops and Snow Day may be getting their own ranked play at some point—though the idea is currently being discussed, not necessarily actively worked on. More of what's ahead can be seen in Psyonix's latest roadmap.
Update: As a Snow Day enthusiast I had to ask, and yep, Psyonix tells me we'll be able to set up tournaments with custom game modes during the beta.