Arfield revealed interest from Rangers first materialised several months ago.
The 29-year-old managed 194 appearances for the Clarets since joining the club in 2010.
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Scott Arfield was happy to sign for Rangers stating that it is a dream.
"I said cheerio to them yesterday but I think I'll be seeing them in three weeks or something", said Arfield.
'If you talk to any midfielder, everyone wants to be like him. His driving from midfield.More news: David Tepper expected to become next Panthers owner
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'Getting that different aspect of off-the-field advice now as well as the on-the-field experience can only enhance you as a player and a person.' He added.
Gerrard spoke of his own joy at making his first ever signing as a manager.
Gerrard said: "I am delighted to have added Scott Arfield to the squad for next season".
The Canada global midfielder has predicted quality players to be attracted to Rangers due to the presence of Liverpool legend Gerrard at Ibrox, and this should be a concern for Celtic.
'It is pleasing also that we have been able to start our rebuilding process so quickly after the end of the season.
Gerrard will initially look to make an impact in the Europa League with Rangers, knowing that steering the Gers through qualifying and to the group stage would be a big early feather in his cap.
The former Basel defender has bags of worldwide, Champions League and top-flight experience that would make him more than good enough for Gerrard at Ibrox.