The former Red believes both players will deliver the goods for the club next season.
The Reds have moved quickly to secure the talented duo, with their contracts set to expire at Manchester City and Burnley respectively.
Milner in particular can be deemed somewhat of a coup for manager Brendan Rodgers, with his experience of winning titles at the Etihad likely to prove vital in a relatively young Liverpool side.
And as far as McAteer is concerned, both will prove to be shrewd acquisitions come next season.
"James is a hard-working player. [He has] plenty of experience now at club and country. He knows what it takes to win things,” he said about Milner.
"I'm sure there were plenty of teams in for that kind of player. He's a top, top professional, lives his life the right way, prepares the right way, and I think he'll bring a lot to the squad and the team."
While Milner is expected to slot straight into the Liverpool first team following his experiences with former Premier League champions Manchester City, Ings is likely to be rotated more at Anfield.
The 22-year-old enjoyed a fine season with the Clarets - scoring 11 goals, an impressive feat for a forward in a struggling side - and was courting interest from a number of clubs, including Tottenham Hotspur - per the Independent.
While it is likely Ings will take some time to adapt to being at a bigger club like Liverpool, McAteer believes he is one of the best available talents in his position.
"[He's a] good young player,” he added.
“Danny was probably, in the second half of the season, one of the bright lights, certainly in Burnley's squad - and looking around at strikers that are for sale, good young talents, then Danny would be up there."