Inoue aims to follow in older brother's footsteps as undisputed champion
The elder Inoue, nicknamed "Monster", became the first undisputed world bantamweight champion in half a century in December, before handing back all four belts the following month to move up to the super-bantamweight division.
The 27-year-old Takuma, two years younger than his unbeaten brother, claimed the WBA bantamweight title for himself when he beat the 41-year-old Solis by unanimous decision after 12 rounds in Tokyo.
He said was happy to "bring the title back" to his family and wants to keep following in his brother's footsteps.
"This is the belt that my brother used to have and it was the first one that he won, so I'm relieved to win it," said Takuma, who was watched by his brother at ringside.
"My brother held all four belts and I want to say that my challenge is now for me to do the same -- I want to become the undisputed champion."
Father Shingo, who trains both brothers, said Takuma would have to step up his training to make his dream a reality.
"He never used to have this goal of becoming undisputed champion but then Naoya achieved it, so Takuma doesn't really have a choice now but to aim for the same," he said.
Takuma, who had to overcome a stray elbow that left him with a deep cut above his eye in the fifth round, took his record to 18-1, winning four by knock-out.
Naoya Inoue is set to contend for two super-bantamweight world titles when he makes his debut in the division against WBC and WBO champion Stephen Fulton of the United States in Tokyo in July.
The fight was originally scheduled for May but was postponed last month when he injured his hand in training.
Naoya Inoue has a 24-0 record with 21 knock-outs, and last year became the first Japanese fighter to top Ring Magazine's prestigious pound-for-pound rankings as the best fighter across all weight divisions.
He also became the first undisputed bantamweight world champion since Panama's Enrique Pinder in 1972 when he beat England's Paul Butler in December.