Bale had been linked with a move away from the Bernabeu this summer due to a lack of first-team football under Zinedine Zidane last term, with long-time admirers Manchester United interested in taking him to Old Trafford.
The Wales international poured doubt over his own future following his match-winning cameo in the Champions League final in May, suggesting that he would seek pastures new if he was not guaranteed a more substantial role in the team.
However, the Daily Mail reports that Bale has been given the reassurances he was after during showdown talks with Lopetegui, and is now happy to stay at the club.
The 29-year-old is expected to be given the chance to take centre stage following the departure of record goalscorer Cristiano Ronaldo, who joined Juventus in a deal worth almost £100m earlier this month.
United had reportedly been willing to significantly improve Bale's wages and offer almost £85m for the winger, although the player's preferred choice was always to stay in the Spanish capital.