The midfielder joined Swansea on deadline day after impressing during his stint with Los Angeles FC, where he made 18 appearances.
O’Brien is set to make his debut for Swansea on Sunday against Bristol City in the Championship.
Ex-Swans defender and assistant manager Alan Tate told the BBC: “Signing Lewis is a good bit of business. He brings enthusiasm and dynamism with the legs he has in midfield. He gets stuck in, he will make passes and he will make forward runs.
“The only way he is like Grimesy is that he is left-footed. They are not like-for-like players in any way really, in terms of how they play.
“Grimes is more of a controller. Lewis is an all-action midfielder who wants to get up and down the pitch. He wants to get forward and score goals but he will also do really well on the defensive side.”