The 28-year-old midfielder spent the second half of last season at Wrexham after three-and-a-half years at Kidderminster Harriers.
Storer has also been on the books of Bedworth Town, Hinckley, Atherstone United, Tamworth and Nuneaton. He made his senior debut for Bedworth at the age of 15.
In 2012/13, he was skipper of the Kidderminster side who went on a remarkable run from bottom of the table in September to finish second in the standings behind champions Mansfield and end the term on 92 points and he played against Sunderland for Harriers in an FA Cup third round tie at the Stadium of Light in January 2014, when he was named man of the match in a 1-0 defeat for the non-league side.
Storer netted 13 goals in more than 150 appearances for the Aggborough club and featured in their two pre-season friendly wins over Cheltenham in the past two years.
Robins boss Gary Johnson, who brought in defender Aaron Downes and midfielder Jack Munns on Monday, said he was highly impressed with Storer's ambition and attitude.
"When I met Kyle I realised how hungry he is to get into the Football League and he is looking for a manager and a club to give him that opportunity," Johnson said.
"I've seen games he's played in and he's a leader. He's been captain at previous clubs and is a strong player and a big character so I am pleased he's signed with us.
"He is a good passer, but he certainly doesn't mind a tackle and he has the ability to dictate games with his positional sense and midfield prowess.
"He can score goals too and I know he'll chip in, but I know he can score more goals and hopefully we'll see that next season."