Police divers recovered the bodies of Damien Little and his two sons from Port Lincoln's Boston Bay on Monday.
Local media said Little, believed to be in his 30s, posted a long suicide note to social media that was later deleted.
Members of the "tight-knit" Port Lincoln community have built a memorial of flowers and toys on the wharf.
"I tell everyone how blessed those children were to have such wonderful parents. I could not fault them in anyway," one neighbour told the Adelaide Advertiser.
"I just loved them. It breaks my heart. It is just so tragic."
Lincoln South Football Club president Brenton Dennis said Little was heavily involved with the local Australian rules football community.
"You couldn't have asked for a better bloke," he told the Australian Broadcasting Corp.
"I've been involved with him through football and I know both families - it's just something that you hear about elsewhere and the way it's touched our community here, it's just indescribable."
Witnesses told police they saw a white Ford station wagon drive off the wharf at speed at around 6am on Monday.
Reports named the children's mother as Melissa Little and described the couple as "doting parents".
A South Australian community is in mourning after a popular young father drove off a jetty at high speed with his two children in the car.