Juneau's staff has handled more than 223,000 calls about the settlement and received more than 97,000 claims. He said 95 percent of claimants who were offered payments by his team decided to accept them.
"I feel this high rate of acceptance reflects the fairness of the settlement amounts as well as the fairness of the claims process," Juneau said in a statement.
However, thousands of people and businesses opted out of the deal to pursue their claims individually.
BP estimates it will pay roughly $7.8 billion to resolve more than 100,000 claims through the settlement, which received U.S. District Judge Carl Barbier's final approval last month. But the settlement isn't capped.
BP agreed to pay $2.3 billion for seafood-related claims by commercial fishing vessel owners, captains and deckhands. Seafood claims are among the $1.4 billion that Juneau's team has paid.
The deadline for claim forms to be filed for the settlement's seafood program is Jan. 22. The deadline for filing all other claims is April 22, 2014.
Barbier gave preliminary approval to the settlement agreement in May 2012.
The agreement also calls for paying medical claims by cleanup workers and others who say they suffered illnesses from exposure to oil or chemicals used to disperse it.
The April 2010 blowout of BP's Macondo well off the southeast Louisiana coast triggered an explosion aboard the rig Deepwater Horizon that killed 11 workers. More than 200 million gallons of oil spilled from the well before it was capped months later.