Boucher, 35, has been forced to retire from international cricket after suffering a serious eye injury in a tour match against Somerset on Monday.
“He’s right up there,” Arthur, the former South Africa coach, told BBC Sport.
“You look at his batting and wicketkeeping stats and they are phenomenal. He’s going to be hugely missed,” he said.
Boucher, the most capped wicketkeeper of all time, was due to play his 150th Test in the final game of the three-match series against England at Lord’s.
He bows out having taken 555 Test victims, including 532 catches – both world records – and 425 dismissals in one-day internationals.
On top of that he has removed 19 batsmen in Twenty20 cricket, meaning Boucher ends his career with a total of 999 international dismissals.
Arthur, who took charge of South Africa between 2005 and 2010, said: “I know he wanted this to be his real swansong of a Test series so it’s really disappointing it ends this way.
“I have so many memories of Mark. I was really close to him, I knew his family really well, we lived in the same city and I coached him at state level.
“I coached him through the period he was out of the South African side (when Boucher was left out of the tour of India in 2004) and helped him get back in so we’ve been through a lot of blood, sweat and tears.
“He is a real guy that you wanted on your side. He never ever gave up and that is how you will remember him.”
Boucher, on his fourth tour of England, was injured standing up to the stumps when a bail hit him in the eye after leg-spinner Imran Tahir bowled Gemaal Hussain.
He had surgery on a lacerated left eyeball on Monday and is due to return to South Africa, with any potential long-term damage to his sight currently unknown.
“It is uncertain for him,” Arthur said. “Let’s just hope he gets that eyesight back and everything is good.”