Police said they had received more than a dozen calls from the Woodside area about Sam Shepherd, 19, and a 17-year-old, who cannot be named for legal reasons, over just a three-month period last year.
The order was issued after the pair were convicted at Telford Magistrates Court for assault.
The 17-year-old was dealt with at Telford Youth Court.
Shepherd, from Willowfield, was given a five-year Criminal Behaviour Order. The 17-year-old was given a Criminal Behaviour Order that will last for three years.
Pc Ian Cole said: "Local residents should not have to put up with the anti-social behaviour of a few individuals and we're determined to do all we can, in partnership with Telford & Wrekin Council and other agencies, to curb the behaviour of those responsible."
The conditions of the criminal behaviour orders include that they must not shout, fight, bang on windows or engage in any dispute that would cause nuisance or distress to any resident across Telford & Wrekin Council.
They must also not cause criminal damage to any property, or use or threaten violence to any person.
They are not use foul, abusive, insulting, offensive or racist language or gestures towards anyone or encourage others to do so.
The pair must not visit any housing scheme for elderly or vulnerable people without prior arrangement by staff.
They also must not associate with Ross Hornby in a public place.