Godden, 24, joined the Fleet from Scunthorpe in 2014 and scored 30 goals in National League South last season.
"I dropped down to Ebbsfleet to rejuvenate and get regular football," said Godden, who has joined on a free.
"The main aim was to bounce back and make a name for myself in the Football League and I thank Darren Sarll and Stevenage for this opportunity."
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The defender, 36, is expected to feature in the final Euro 2016 warm-up friendly against Slovakia in Trnava.
If he is selected by manager Michael O'Neill, he will become only the second NI player to hit the century mark along with legendary goalkeeper Pat Jennings.
"It's something no-one can ever take away," Hughes said.
Hughes made his debut against Slovakia and is now poised to reach his century against the same nation after earning his 99th cap coming off the bench in last week's 3-0 victory against Belarus at Windsor Park.
The former Aston Villa, Newcastle United and Fulham player retired from international football but was persuaded to return in 2012 by Michael O'Neill.
"At one point I never thought I would do it [100 caps] but Michael came back in and he said a few things that really resonated with me.
"He made me really think about it and I thought 'you know what, that would be quite something'."
The former Northern Ireland captain was also inspired by playing alongside two centurions at Fulham, the Republic of Ireland's Damian Duff and Greek midfielder Georgios Karagounis.
"Damian had just got his 100 and Karagounis was there too so I was sat there with a couple of lads who were sitting there with a hundred caps and I thought it would be pretty cool to have that.
"To walk away at the end of your career and look back on it, it's something no-one can ever take away so I feel a great deal of pride.
"The amount of help I've had over that period from a lot of different people it would be too long to say thank-you to everyone but I'm very grateful to everyone who's helped along the way, and Michael has played a big part in that."
Northern Ireland open their Euro 2016 campaign against Poland in Nice on 12 June.

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Ebbsfleet striker Matt Godden has become Darren Sarll's first signing as full-time manager of Stevenage.
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Aaron Hughes says he never expected to earn 100 caps for Northern Ireland and will feel 'a great sense of pride' if he reaches the milestone on Saturday.
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