The Wales boss cited his time playing with Solskjaer at Old Trafford and stated people have the wrong idea about the Norwegian.
Solskjaer has appeared relaxed and composed since arriving in Manchester last December, but Giggs told the Daily Mail's Ian Ladyman the 46-year-old possesses a driven and competitive character.
Giggs recalled Solskjaer's comment to Rio Ferdinand soon after the defender signed from Leeds United in 2002.
When Ferdinand lost control of a long pass in training, Solskjaer told the new record signing: "Is this all you get for £30 million these days?"
"See, he's not the nicest bloke in the world like people say he is and that's because we rubbed off on him," said Giggs. "Ole was the nicest guy in the world until we got hold of him. When you got in that environment with us it was a tough school and you changed. You had to. That day with Rio we were just testing a new player and if Ole hadn't said it then someone else would have. That's what it was like. Every day. It helped us to win."
United have been rejuvenated under Solskjaer, and the team has played some of their best attacking football since the retirement of iconic manager Sir Alex Ferguson in 2013.
The Red Devils were miles off the Premier League pace for the top four under former coach Jose Mourinho, but they are now only two points behind a UEFA Champions League qualification spot for next season.
Solskjaer has empowered his side to drive forward and score goals, playing the brand of football the former striker was taught under Ferguson.
Giggs added he did not know who Solskjaer was when the Scandinavian was signed by United in 1996, but after his first session working with the Norwegian, he told friends he had "just trained with the new [Alan] Shearer."
United are yet to appoint a full-time manager for next season, but Solskjaer has given the perfect audition if he desires to stay in Manchester.
He has led his team into the quarter-finals of the Champions League, and United have the chance to record a memorable finish to what had initially been a campaign to forget.