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McCullum's appointment was confirmed on Thursday after two days of interviews at the start of this week and Strauss, who was part of the interview panel along with CEO Tom Harrison, performance director Mo Bobat and managing director Rob Key, said that he was "delighted" with the decision.
"I was involved with the interview process and he knocked it out the park," Strauss told talkSPORT at the Sports Industry Awards on Thursday night. "But these appointments aren't about interviews. They're about approach, really, and about the reputation that people have and I know he's the sort of guy that the England players will look up to and he'll be able to show them the way.
"He's done that with New Zealand cricket as captain, he's done that in the short-format tournaments he's been involved with. I think he's going to make a massive impact on English cricket. He's got such clarity of thought and approach.
"He's a guy who keeps the game of cricket very simple but he's got a positive intent in everything he does and that's exactly what the England Test team need right at the moment: some good, strong leadership, some direction. I know Brendon is just so excited about the prospect of coming out here and not just trying to take the English cricket team forward but also doing his bit to take Test cricket forward generally."
Strauss added that McCullum's appointment felt "nicely connected" with the positive approach espoused by Key and Ben Stokes, England's new Test captain, and suggested that they would make some changes in personnel when the squad to play New Zealand at Lord's on June 2 is announced next week.
"The first thing is about mindset, and embedding that mindset in the players," Strauss told Sky Sports at the same event. "There might be a couple of selection changes, players that play in that style naturally, I would have thought. But the most important thing of all is the connection and alignment between him and Ben Stokes, the captain: them forging a strong, productive relationship is going to be crucial.
"He's a very positive guy with a very clear mindset and he will embed that in that Test team at a time when confidence is a bit low and people need a bit of clarity and direction. He's an impressive guy. He can't wait to start - and quite frankly, I can't wait for him to start.
"He was just unbelievably ambitious [as a player]. He used to run down the wicket against some of the quickest bowlers in the world, he always took the positive option, he wasn't scared of failing.
"He wasn't scared of making mistakes and I think that's what this Test team needs a bit at the moment. They need someone to back them, they need someone to give them confidence and inspire them and they need to actually break the shackles and realise how good they are and I think he's the perfect person to do that."