After an Arena/Colosseum season concludes all Guardians are able to claim the end of season rewards from the Arena/Colosseum lobbies. A season encompasses a week, from Monday to Sunday, and the rewards will be distributed on Monday the following week. 

There is an in-game countdown that displays the remaining time of the season. Both Arena and Colosseum seasons start and end at the same time:

As a reminder, please keep in mind that in order to be eligible to receive the Arena or Colosseum rewards you need to participate in at least one battle during the season.