Hello, Anonymous.
Ideally, the answer to this question should be in the Settlement Agreement. I'll assume it is not, otherwise you probably would be asking.
There's no general set-in-stone rule regarding how long you are required to store your ex's belongings. That's why the best option is probably to file a motion asking for the Court's permission to dispose of his belongings. This way you will have brought issue to the Judge's attention; you will presumably be given permission to dispose of them; you won't have to worry about any consequences from improperly destroying his property (improperly disposing of another's property can cause you to be held liable for the value of the property you destroyed); and if you have incurred any costs from holding the property for him, you may seek to be compensated for your troubles.
It should be a fairly quick and simple court appearance. If he wants his stuff, he can come and claim it. If he doesn't show up or tries to delay things, the Judge will likely be more willing to give you permission to dispose of the property.
I hope this helps.
Answered on Jul 14th, 2015 at 3:55 PM