For once, the literal translation works:

• "Ravi de l’entendre" ou
• "Je suis ravi d’entendre ça"

Or, as suggested by @Damien, since the news could have been bad but turned out to be good:

• "Je suis soulagé de l’entendre"
• "Je suis soulagé d’entendre ça"
• "Quel soulagement!"

(soulagement = relief)