Sinisterra, 24, who scored eight goals in 25 games for Leeds since joining last season, is the Cherries' eighth signing of the summer.
The deal includes an option to buy the Colombian, who has three goals in seven appearances for his country.
Englishman Anthony, 23, has scored 11 goals in 91 games for Bournemouth.
The former Arsenal youngster is Leeds' ninth arrival of the summer.
Speaking about Sinisterra's arrival, Bournemouth chief executive Neill Blake said: "He's a player that has already experienced Premier League football and has featured at the top level in Europe too, so we're really looking forward to having him with us."
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