The 25-year-old is set to join from Kaiserslautern and has been granted a work permit.
The Swans are still waiting for the formalities of the deal to be finalised by the German club, but the German club have given permission for Shechter to feature this weekend, with the move set to be completed in the coming days.
Shechter told the club website: "I'm very happy. "It will be a dream to play in the Premier League because it is the best in the world."
Shechter, who watched the mid-week friendly win over Blackpool, added: "The manager (Michael Laudrup) was also a big draw for me. Growing up watching him play was unbelievable. For me he was the top player in the world playing at the best clubs, like Real Madrid and Barcelona, where he was also a champion.
"I'm looking forward to working with him and playing for Swansea. I've only been here for two or three days, but I already have a good feeling about the club. It's a family club and everybody has been so warm and friendly to me.
"I watched Swansea a few times on TV last season and I liked their style. There is a big Spanish influence with their style of play which I think will suit me. I'm not the tallest of players, so anything on the grass is good for me.''
Once the deal is completed Shechter will become Laudrup's fourth summer signing following the acquisitions of Chico Flores, Jonathan de Guzman and Michu.
Shechter, who has 13 caps to his name, moved to Kaiserslautern last summer from Hapoel Tel Aviv, but scored just three goals as they were relegated from the Bundesliga.
But he believes he can put those struggles behind him at the Liberty Stadium.
"If I'm honest, last season wasn't a good one for me because we were relegated and I didn't play as much as I would have liked,'' said Shechter.
"I spent a lot of time on the bench, but I have confidence in my ability and I want to do well at Swansea. I know I will have to work my way into the team, but it's about the club and not me.
"The club did very well in their first season in the Premier League. The second one is always more difficult, but I hope I can still help make it a better one.''
Laudrup still hopes to add a winger to his squad and will need to find reinforcements in midfield as Joe Allen heads to Liverpool in a £15million switch.
Bolton's Mark Davies is known to be among those interesting the south Wales club.