"Que" is the object of "m'ont confié", and it stands in for "les contrats" which is plural. The basic rule of agreement for past participles conjugated with "avoir" is that they agree with the object when the object is placed before the verb, which is the case here.
You would also say: (using emphasis to indicate the object of m'ont confié):
Des souverains m'ont confié ces contrats.
Object after the verb ==> no agreement.
Ces contrats, des souverains me les ont confiés.
Des souverains me les ont confiés, ces contrats.
Object before the verb ==> agreement.