Artist Dave Cockrum had already famously re-designed most of the members of the Legion of Super-Heroes, giving them modern revamps to their rather staid older costumes. His Lightning Lad re-design was particularly good, as while many of the character got later revamps over the years, Cockrum's Lightning Lad look became a standard one for the character for decades. Essentially, Cockrum was so far ahead of the game that when the team was revamped in the 1990s, his early 1970s design fit right in. While working on the Legion, Cockrum designed a new team of heroes called the Outsiders who were set to team up with the Legion. DC passed on the concept.
Mike Zeck came up with the actual look and it is a stunning piece of design. All black except for the prominent white spider. Rick Leonardi also did some tweaks to the costume and it soon became the most controversial, yet surprisingly popular costume change in comic book history. Fans were aghast at first but then really started to enjoy the new look. Eventually, the design was adapted for the villain Venom, with Spider-Man returning to his classic look. It is popular enough, though, that it still makes occasional comebacks.