In 2012, Bournemouth began their third successive campaign in League One, but under Eddie Howe, they have secured two promotions in three years, and the Cherries are currently holding their own among English football's elite clubs.
On Tuesday night, goals from Steve Cook and Benik Afobe earned Bournemouth a 2-0 victory over South-Coast rivals Southampton, and although they struggled for opportunities during the second half, Redknapp was pleased that the team were able to prove that they had another string to their bow.
Southampton created just one clear opportunity through the 90 minutes - an early effort from Charlie Austin from 10 yards - and Redknapp, a former player and manager at the Vitality Stadium, suggested that those kind of performances are what transformed the club from a mid-table League One outfit to a team capable of surviving in the top flight.
Redknapp said: "They aren't just a pretty side. You don't come out of the two divisions that they have if you can't do the other side of the game.
"They dig in, they work, they close down, they can play. They are a very good side. They willingly work for each other."
The win for Bournemouth moved them eight points clear of safety in the standings, and if they can get the better of Newcastle United at the weekend, they will be within touching distance of confirming their Premier League status for a second season.