The 28-year-old was a free agent after leaving Exeter's biggest rivals at the end of his contract in the summer.
Reid has also played for Yeovil Town, West Bromwich Albion, Brentford and Rotherham United.
He scored a hat-trick against Exeter in the Devon derby in 2015 - the first in the fixture since 1929 - and could make his debut for the Grecians against Argyle in League Two on Saturday.
Reid scored 21 goals for Argyle during the 2013-14 season while on loan at Home Park and 20 the season after.
But last term he managed just seven goals as he was hampered by a foot injury, later telling the BBC that his season had been a 'write off'.
Exeter need more firepower, having scored just six goals in the league so far this season, with half of those coming in their 3-2 victory at Colchester earlier this month.
"I have been in talks with a few teams, but I met the manager (Paul Tisdale) on Sunday in a nice pub in Bath and he explained what he wanted to do for me," said Reid
"I went home feeling refreshed and it left me with a massive smile on my face. I just couldn't wait to get the deal over the line."
"I played against his teams for years now throughout my career and Exeter, whether they have been in the division above or League Two, have always been good on the eye to watch," he added.

However, it could not confirm whether they were the "skulls of beheaded heroes" which President Robert Mugabe referred to earlier this week.
Zimbabwe's leader had demanded the return of those killed by the British in the late 1890s during the first uprising against colonial rule.
He made the remarks at the shrine to remember the country's war dead.
"We are told that skulls of our people, our leaders, are being displayed in a British museum and they are inviting us to repatriate them," he told the crowd.
"We will repatriate them, but with bitterness, questioning the rationale behind decapitating them."
Known as the heroes of the "First Chimurenga", they were defeated by the British after a protracted battle and the ringleaders were tried and hanged.
What happened to their bodies has always remained a mystery.
Zimbabwe's liberation struggle:
The UK Foreign Office has now confirmed that talks have been going on since December 2014 over the "potential repatriation of Zimbabwean human remains".
It said technical experts from Zimbabwe have been invited to meet their museum counterparts in London.
"We await the appointment of the required Zimbabwean experts in order to take this forward," the statement said.
But the BBC's Africa correspondent Alastair Leithead says it is not clear if the remains are of the rebellion leaders.
The Natural History Museum, which has a collection of 20,000 human remains, said it "actively engages in discussions with governments and communities" over requests for the return of human remains.
More from the BBC's Alastair Leithead on Zimbabwe:
Triumvirate retains firm grip on power
Exeter City have signed former Plymouth Argyle top scorer Reuben Reid.
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The UK's Natural History Museum has said it may hold Zimbabwean human remains in its collection.