Saudi Arabia has sidelined its veteran intelligence chief, Prince Bandar bin Sultan, as leader of the kingdom's efforts to arm and fund Syrian rebels, replacing him with another prince well-regarded by U.S. officials for his successes fighting al-Qaeda, Saudi royal advisers said this week.

The change holds promise for a return to smoother relations with the U.S., and may augur a stronger Saudi effort against militants aligned with al Qaeda who have flocked to opposition-held Syrian territory during that country's three-year...