Dyson, who is 4-1 this season with a 2.47 ERA and 47 strikeouts in 51 innings, was traded by the Giants to the Minnesota Twins. In return, Minnesota gave up right-handers Prelander Berroa andKai-Wei Teng and outfielder Jaylin Davis.
Melancon agreed to waive his no-trade clause after discussing things with his wife.
"After we talked and realized it's Atlanta, a really good situation over there, we decided it's OK," said Melancon, who is 4-2 with a 3.50 ERAin 43 appearances and 46 1/3 innings this season. "It's a winning team. They got a lot of young talent, a lot of upside there."
Giants presidentFarhan Zaidi said the team's depth throughout its system allowed the team to make the trades.
"I would say this is in some ways an endorsement of the depth of some of the guys we have right behind the group that has done so well for us at the major league level," Zaidi said. "... Unsurprisingly, there was a lot of demand for our relievers. It would have been difficult to make some of these deals without the feeling of confidence we have in the guys who are going to be coming up right behind them who have been pitching so well in Double-A and Triple-A this year."
Pomeranz provides Brewers manager Craig Counsell with options. The lefty is 2-9 with a 5.68 ERA in 21 appearances with 17 starts this season. He moved to the bullpen and made four scoreless relief outings most recently.
He had his best season in 2017, when he went 17-6 with a 3.32 ERA for Boston.
Brewers president David Stearns said the plan is to use Pomeranz primarily as a reliever.
The acquisition of Dyson is another move by the Twins in recent days to strengthen their bullpen. Minnesota acquired reliever Sergio Romo from the Marlins on Saturday.
:"This is a very nice acquisition for us," Twins manager Rocco Baldelli said. "He's a hard-throwing guy, a guy with very good command. His fastball is a weapon in itself. I don't know if he calls it a sinker or a two-seamer, but I think he gets great action on that pitch. This is a guy that's done it. He's had a lot of success. He's a guy we're going to turn to in later-innings situations, and I'm excited to be able to call his name.''
Black has spent the bulk of this season at Triple-A Sacramento, where he was 1-0 with a 5.16 ERA.
Dubon was one of the Brewers' top prospects, a middle infielder who hit .297 with 16 home runs and 47 RBIs at Triple-A San Antonio.
Information from The Associated Press was used in this report.