This convertible tiara/necklace is not a royal family heirloom - as Tartucat stated here correctly, it was newly aquired in 1986 and given as as gift to Queen Silvia from her husband on their 10th wedding anniversary.
(Therefore I always thought it should be called 'Queen Silvia tiara' rather than 'King Carl Gustaf tiara' - I never would expect HIM to wear it!)
I would love to know if it was first designed back then or if it's an older piece that the King bought, but no info has ever come up about its provenance.
IMO it's lovely both as a necklace and a tiara. Maybe the nicest 'new' tiara around, among all the new tiaras that were added to some Royal collections over the past 20 years. It always looks great both on Princess Madeleine and Queen Silvia and yes, CP Victoria has worn it too but only as a necklace. It's a very classy and timeless piece.