Robert Cowper and Willie Guild led the operation which tracked and arrested Benat Ordonez in Edinburgh in 2012.
Ordonez was accused of being part of the Basque separatist group Eta, which has waged a bloody campaign for independence from the rest of Spain.
He was arrested by police in Leith and was wanted by both the Spanish and French authorities.
Mr Cowper and Mr Guild will travel to London on Friday to receive Spain’s police merit cross at a ceremony which will be attended by the Spanish ambassador and the head of the country’s Guardia Civil.
Ordonez had been working as a van driver when he was arrested outside a pub on Leith Walk.
Mr Cowper, 52, now a retired detective chief inspector, was acting as a temporary superintendent at the time of the operation.
He said: “We were able to track him down fairly quickly, but other than that I can’t go into much detail.
“He had been living and working in Edinburgh and carrying on as a normal citizen. There was no evidence he was carrying on any of his [Eta] activities here.
“The guy was living a pretty normal existence here and it wasn’t difficult to catch up with him. Two members of my team managed to jump on him outside the pub – it was a pretty straightforward arrest.”
Mr Cowper said he was proud to receive the prestigious honour, but stressed he was picking it up on behalf of all the other police officers who also worked on the case.
“I see myself as representing the whole team,” Mr Cowper said. “Willie and I led two teams to track down and carry out the arrest.”
Ordonez had lived in the UK since 2001, but was sentenced to five years in jail by a French court in 2008 for an alleged conspiracy to carry out acts of terrorism.
Spain also sought Ordonez’s return so he could be put on trial over his alleged membership of, and collaboration with, an “armed organisation”.
At a hearing in the High Court in Edinburgh in 2012, it was claimed Ordonez was part of a group which helped move materials and weaponry from France to Spain.
It was also alleged that he was involved in gathering information on politicians and police officers.
Ordonez initially fought his extradition, but later dropped his opposition to returning to France – a move which the Spanish authorities agreed to.
The Spanish Interior Ministry said previously: “Everything suggests he was part of Eta’s reserve apparatus, groups formed by fugitives who are prepared to form active cells when the terror leadership decides.
“He joined Eta in 1996 as a member of their transport command.”