The 36-year-old had been in talks with Boca President Daniel Angelici for months but failed to come to terms over a contract and will be unveiled as an Argentinos player on Saturday before linking up with his new team-mates next week.
Riquelme, who began his career with the club based in the La Paternal district of Buenos Aires, was confirmed to be arriving by Borghi.
"It's all arranged with Riquelme - he should be with us on Monday," the former Chile boss told Fox Sports.
"It is an honour and a pleasure to have him - he is extraordinary. The club will have to change. It's going to be historic for Argentinos. Here he will find affection and will be treated well."
Borghi, who is a friend of the midfielder, played a key role in bringing the former Barcelona man to the club having worked with him at Boca, and he revealed that the playmaker is not joining simply for money.
"With Roman I have a relationship of respect and admiration," the 49-year-old continued.
"The last time I saw him we spoke for six hours about football. Yes, we are friends.
"We had several meeting with him where we appealed to human and football identity arguments over economic ones.
"The passage of time comes for everyone, but the quality is not lost. He is going to be an essential example for the youngsters to copy."
Argentinos now play in the Primera B Nacional, Argentina's second tier, after being relegated last season.