Media mogul Sumner Redstone and his family have agreed to settle their long-running legal dispute with his former live-in companion, Manuela Herzer, less than a week before one of the cases was scheduled for trial in California, according to people familiar with the matter.

As part of the settlement, Ms. Herzer has agreed to pay back $3.25 million of the tens of millions of gifts that Mr. Redstone gave her, the people said. The wide-ranging agreement ends all litigation between the two sides, who have been battling in the...