Presale for the new dates begins on December 3, before the on-sale opens three days later on December 6 at 10am local time.
The residency now totals 32 shows over 16 weekends. It began on September 20 and is currently due to end on April 12 next year.
Tickets for the new dates start at $175 (£140/€165), with the pricing inclusive of taxes and fees.
Limited VIP ticket packages will also be available and include premium seats, exclusive merchandise, and parking.
Irish rock band U2 opened the Sphere in September last year with a residency that ran until March, featuring 40 shows.
The Eagles are the fourth band to feature at the Sphere, with Phish and Dead & Company also headlining the venue. Dead & Company’s 30-night residency came to a close in August this year.
The $2.3bn venue can hold up to 18,600 guests and boasts floor-to-ceiling graphics and a 580,000-square foot exterior exosphere.
The Eagles’ next show at the Sphere is set to take place on December 6.