With Adam Tann leaving at the end of last season and Phil Picken returning to Chesterfield following his loan spell at Meadow Lane, bringing a right-back to the club has been a priority for Magpies manager Ian McParland.
The Scot has been tracking Moloney for some time and he is delighted to finally sign the Republic of Ireland international.
"Brendan is a very promising young player and he has been a target of mine for a while. In fact, I tried to get him in last season but we couldn't finalise a deal," McParland told County's official website.
"It is nice to have finally landed him and I believe we have a player on our hands who is more than capable of performing at this level.
"When I saw him play for Forest's first-team last season I thought he was one of their best players. I have always kept my eye on him and I am really pleased to have him on board."