This feature is available in all editions.
In Agile, backlog is assigned to the team, not to team members.
In Lifecycle, this is typically done during the strategic planning stage. There are two ways to assign work to a team:
On the Team Scheduling page, click on a backlog item to open the details view and select the team.
Later, in Detail Planning (Sprint Planning > Detail Planning), members are assigned to work items from the team's backlog. In this way, they are implicitly assigned to the team. See Assigning Members to a Team below.