Strauss announced his retirement from cricket on Wednesday, having informed his teammates via individual handwritten letters after the one-day side's defeat against South Africa on Tuesday.
Finn has known Strauss since he was a teenager, bowling to him in the Middlesex nets and going on to become a teammate at county and international level.
He said it is a sad time to see the 35 year old depart, but praised him for a hugely successful three-and-a-half year stint at the helm.
"It's obviously disappointing to see Straussy leave us as captain and leave cricket altogether," said Finn. "He was a fantastic captain and it was great to play with him for Middlesex since I was 16 or 17 years old. To grow up with him around has been fantastic. He's achieved so much in an England shirt and been such an inspirational leader for the group and for me personally.
"He was a masterful captain in the way he went about dealing with those sorts of things."
Alastair Cook, who took over the one-day captaincy from Strauss after last year's World Cup, has inherited the Test reins and Finn has no doubt he will be a success.
"Moving forward Alastair has done very well as one-day captain and we've played a great brand of one-day cricket under him," he said. "We're looking forward to doing that in the Test matches now."
Cook's immediate focus, however, is on squaring the NatWest Series against South Africa at The Oval tomorrow.
He said he was "incredibly proud" to be the new England captain. "It's a huge honour for me and I'm very excited about the challenge," he said.
Before he takes charge at Test level England still have three one-day games against the Proteas.
"It is back to trying to win a very important series against a very good side," Cook said.
"After that series I will sit down with Andy Flower [the England coach] and discuss what we are going to do."
That is sure to involve talks on whether or not the out-of-favour Kevin Pietersen will be welcome in the squad and, secondly, who should partner him at the head of the innings in Strauss's absence.
Cook was not ready to identify potential candidates but said: "It feels like all my England career I have walked out to bat with Straussy. That's a huge hole to fill."
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