The 32-year-old has joined the Pilgrims from Saturday’s opponents York City, having previously represented the likes of Oxford United, Mansfield Town and Torquay United.
Heslop is working his way back to full match fitness following an injury lay-off but is available for selection with immediate effect.
Reflecting on Heslop's arrival, Elliott told bufc.co.uk: "Simon brings a wealth of experience and aggression to our midfield that we perhaps lack.
"I have kept an eye on his progress for a while. He's coming back from an injury so slowly he might need building up in the first few games but his passion to be successful with a team and get back to his own personal high standards was obvious after speaking to him and watching him train with us last week.
"I had him watched recently against Whitby Town and the report was he was outstanding, so it seemed a perfect fit for us both."