The eagles were captured during the battle, not hidden by the legions. The eagles were captured by certain tribes out of Arminius' confederation, the Bructeri, Marsi and Chauci respectively, and taken with them to their own lands.

• The eagle of the legio XIX was captured by the Bructeri, who lived on the upper Ems in modern southwestern Lower Saxony. This eagle was recovered in the year 15 by a unit led by Lucius Stertinius, one of Germanicus' subordinates, when he devastated the bructerian countryside after defeating them in battle:

The Bructeri, who had set their belongings on fire, were beaten bei L. Stertinius with a unit (marching) without baggage at Germanicus' command, and during the murdering and plundering he recovered the Eagle of the 19th legion, which had been lost with Varus. [Tac. Ann. I, 60.3]

• The eagles of the Legio XVII and XVIII. The first of the two remaining eagles was recovered from the Marsi during the expedition of Germanicus in the following year. Tacitus doesn't mention to which legion this eagle belonged:

Personally, he [Germanicus] invaded the territory of the Marsi [between Rhine, Ruhr and Lippe rivers in modern Westphalia] with an even greater force, while their leader Mallovendus, who had submitted himself shortly before now stated that one of the eagles of the legions of Varus was buried in a nearby grove, and was only lightly defended. Immediately a unit was dispatched to draw out the enemy in front, while another one was to go around the enemy in the back and dig up the ground, and both units were aided by luck [that is to say, the enemy was defeated and the eagle recovered. Tac. Ann. II, 25].

• The last remaining eagle was only recovered later during the reign of Claudius in the year 41, when Aulus (sometimes also Publius) Gabinius led an expedition against the Chauci, who settled at the coast of the North Sea between Elbe and Ems (modern East Frisia):

This same year, however, Sulpicius Galba overcame the Chatti, and Publius Gabinius conquered the Cauchia and as a crowning achievement recovered a military eagle, the only one that still remained in the hands of the enemy from Varus' disaster. Thanks to the exploits of these two men Claudius now received the well-merited title of imperator. [Cass. Dio LX, 8]

What exactly they did with them is unclear, but it seems that they were stored in sacred groves, mirroring their use in the Roman legion where they were revered as deities and stored in a sanctuary, often together with statues and images of the emperor and the vexillae, the other standards; but Arminius and his Cherusci seem to have captured none of the Eagles. During the reign of Augustus, the recovered standards (signa recepta) were an important propaganda asset. Augustus had already recovered the eagles that had been lost to the Parthians in 20 BC, and erected a temple (the temple of Mars Ultor, or Mars the Avenger) to store them in on his new forum. Coins were minted that showed the temple together with the recovered Eagle and other standards. Similarly, the Eagles recovered from the Germans were celebrated as well. An arch was dedicated to Tiberius next to the temple of Saturn that celebrated the recovery of two of the Eagles under his command ("At the end of the year an arch was erected next to the temple of Saturn as thanks or the recovery of the standards lost with Varus under the leadership of Germanicus and the command of Tiberius" Tac. Ann. II, 41). Similarly, after the death of Germanicus in 19, three arches were erected in his honour, the one on the Rhine carrying a statue of Germanicus, showing him receiving back the Eagles from the defeated Germans:

[... supraque eam ianuam statua(?) Germanici Cae]/saris constitueretur recipienti[s signa militaria ab Ger]manis...