It's not clear.
Previously, I thought that Saito entered Limbo before Cobb, and that would explain everything. This agrees with this, this, and many others.
However, the proper order of events is:
- Fischer dies in level-3 (reaching Limbo)
- Cobb and Ariadne sleep in level-3 (reaching Limbo)
- Saito dies in level-1 (reaching Limbo)
- Mal stabs Cobb in Limbo and gets shot
- Ariadne and Fischer kill themselves in Limbo (riding layers of kicks and reaching level-1, and eventually reality)
- The van in level-1 sinks with Cobb and Saito, everyone else hides somewhere safe
- Cobb finds Saito, very old, and both kill themselves (reaching reality)
So, what happened in that missing period? There are a few theories, and two of them seem equally likely to me.
Cobb was there for a longer time, but knew it was Limbo, so didn't age.
From here, the idea is that Cobb just didn't allow his projection to age, because he knew he was dreaming. Unlike Saito, who died, and thus thought Limbo was now his reality. Cobb took years to find Saito, hence Saito's age.
Cobb drowns in level-1 and returns to Limbo (after many years from Saito's perspective).
From here and here, Cobb either dies from his stab wounds and goes up to level 1, or just remains in Limbo. When the van in level-1 sinks, Cobb drowns, and re-enters Limbo. At this point, he has entered Limbo years after Saito. In the movie, we see that the scene right after the van sinks is with Cobb waking up on the beach.
Other theories include:
level-4 not being Limbo, so Cobb dies and reached Limbo there. Doesn't explain why Fischer dies and gets to level-4 instead of Limbo, though.
Different Limbos. Cobb and Ariadne first enter Fischer's Limbo, and then Cobb enters Saito's Limbo.
For historical reasons, here is my previous answer:
Saito died in the 3rd level dream a few minutes earlier than Cobb. In limbo, that amounted to years and years of waiting, which is how he got so old.
This website has a great explanation of the levels and limbo.
THE MINUTES IN LEVEL THREE BETWEEN SAITO AND COBB ENTERING LIMBO HAVE FELT LIKE DECADES IN LIMBO AND SAITO IS AN ELDERLY MAN.