Roche's volley for Peamount United against Wexford Youths in a Irish league game watched by fewer than 100 spectators became the first goal scored by a woman to be named a finalist in the FIFA Puskas Award
for goal of the year.
"I am so excited about the signing of Stephanie, we are getting a player that has great technical ability, a superb left foot, and possibly the best goalscorer to come out of Ireland since (former international striker) Olivia O'Toole," Dash head coach Randy Waldrum said on the club's website.
"Stephanie will bring a wealth of international experience to our team, and another great attacking option that is different from what we have already," he added.
"All our Dash fans and fans of women's soccer in general will be excited about this signing."
James Rodriguez won the Puskas Award for 2014, but the Colombian was gracious enough to say that Roche's fabulous volley, which took second place at FIFA's glitzy ceremony in January, just might have trumped his goal against Uruguay at the World Cup last year saying it "deserved to win, but only one can."
Rodriguez's goal came in front of thousands at Rio's Maracana Stadium, with millions more around the world watching on TV.
It was a very different setting when Roche collected the ball with her back to goal, flicked it over her head and crashed it home while playing in the Irish Woman's National League.
Nevertheless, her brilliant goal, filmed by chance, beat Robin van Persie's flying header for Holland against Spain at the World Cup into third place.
Victorious Real Madrid forward Rodriguez hailed Roche's effort as "a golazo" (an amazing goal), while Italy legend Alessandro del Piero described her as the "moral winner."
"She is great," Del Piero added. "She needs to score another one for next year. That is what I would say to her."
The FIFA award, voted for by the public, saw Roche take 33% of the vote, with winner Rodriguez on 42% and Van Persie some way back on 11%.
Roche first represented the Republic of Ireland when she was 14 years old playing for the Under-17 team, and has since earned 35 senior caps
for her country.
The 25-year-old's move to America follows a brief stint with French club ASPTT Albi where she struggled with the language barrier according to the Irish Times
Roche's boyfriend Dean Zambra, who plays for League of Ireland side, Bray Wanderers, will join her in the U.S. for three months to help the striker settle in.
"I've been given a huge opportunity by Houston Dash and I'm hoping I'll be able to go over and do well and hopefully be successful over there" Roche told RTE Radio. No terms of the deal have been revealed.