The first WCW World Tag Team Champions were Doom, who held the version of the NWA World Tag Team Championship that was created by Mid Atlantic Championship Wrestling and subsequently recognized by WCW. This version of the NWA World Tag Team Championship was renamed the WCW World Tag Team Championship in January 1991. From July 1992 to September 1993, the WCW World Tag Team Championship was unified with the current version of the NWA World Tag Team Championship, but the titles were split when WCW left the National Wrestling Alliance.
After the NWA had split with WCW, the NWA created their own World Tag Team Championship, and WCW continued using the unified Mid Atlantic version Tag Team titles, adding more prestige and new reigns to the title's history.
NWO's championship invasion extends to the WCW Tag titles
But however, after the New World Order was formed in 1995, wrestlers on WCW's side rarely get to win the Tag titles as NWO members always got opportunities at the titles because of one reason: Eric Bischoff, the third and final President of the company was a NWO sympatizer and allowed no wrestler on WCW's side to win any WCW championship from NWO members. Also as a result of any NWO member winning the WCW Tag Team Championships, the titles were unofficially renamed the NWO World Tag Team Championship.
Vince Russo's failed attempt
When Vince Russo came to WCW, he attempted to bring the prestige and credibility back to the company's Tag Team titles by stripping all NWO members of all their titles when they reformed in mid-2000 and giving equal oppotunites to any wrestler whether they represent the NWO, WCW, young or old to challenge for the titles.
But Russo's attempt failed and he left WCW a year before the company was purchased by the WWE (then known as the WWF).