Racchi, 31, began his career at Huddersfield and has also played for Bury, York, Kilmarnock and Icelandic side Valur.
He started last season with Curzon Ashton before joining Hednesford Town.
Manager Paul Rawden said: "Danny is the first of many names we'll see coming into the club. He's got bags of experience at a higher level, he's what we need in the middle of the park.”
Tempest, 25, joins from Matlock Town, having joined them from Basford midway through the season.
He said: "I came here twice last season (both defeats) and the support I heard from the far side was brilliant.
“They did a great job in making things uncomfortable when I came with Basford. Paul has told me that they were backed all the way home and away.
“That's a big factor in being sold somewhere. It's all about getting started now, pre-season is going to be hard work. The friendlies we've got lined up are good ones.”
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