Yes, patch 5 has added a storage mechanic to the game.
In the Undercroft of Skyhold, where you manage your weapons and armor, there is a chest where you can store up to 1000 items. You can only store weapons, armor, accessories and upgrades.
Prior to patch 5 at the beginning of March 2015, there was no storage mechanic in Dragon Age: Inquisition.
BioWare had confirmed on November 19, 2014 that they knew DA:I players were requesting the feature, but hadn't made any promises.
QA member Bryan Johnson:
"We have noticed this is a fan want. Not sure if it will happen, but it has been acknowledged we have seen it."