The boys, both from West Yorkshire, were spotted by plain clothed officers targeting drug dealing in the town last Thursday.
The officers became suspicious of their behaviour and approached the boys, who initially ran off from them, before they were detained following a short chase.
The pair were searched under the Misuse of Drugs Act and two Kinder eggs containing suspected heroin and crack cocaine were found along with a knuckle duster seized from one of the teenagers.
The boys are believed to be involved in county lines drug supply into Harrogate.
The 16-year-old was arrested on suspicion of possessing class A drugs with intent to supply, possessing cannabis and possessing an offensive weapon.
The 15-year-old was arrested on suspicion of being concerned in the supply of class A drugs.
Both have been released on conditional bail to allow for further enquiries to be carried out.