The Border Harrier, from Scotby, came in behind Scot Andrew Butchart who surged clear of the field to win and seal his place in the GB team.
Butchart broke away with four laps to go and enjoyed a celebratory final lap as he finished in 13mins 44secs.
Farrell pipped fellow Englishman Andy Vernon for second place. The 25-year-old represented GB at the 2015 World Championships in and 2016 IAAF World Indoor Championships.
After the event, Farrell, who won the British Championship in 2015, Tweeted: “Mixed emotions with today’s race, over the moon to punch that ticket to Rio. Head down for the next 7 weeks.”
Meanwhile, Scotby’s Nick Miller could only finish third in the hammer.
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