On the same day as 21-year-old midfielder Spittal arrived from Championship side Dundee United, it is understood that Lindsay was in England for transfer talks with Oxford United.
The highly-rated 21-year-old centre-back has two years left on his current deal at Firhill and is expected to cost the League One outfit around £350,000.
That fee could rise with performance-related add-ons and clauses for a player who was voted into the PFA Scotland Premiership team of the year last season.
Spittal, who started his career at Queen’s Park, revealed he had been impressed with Thistle’s style of play.
He told Jagzone: “Having played against them in the past, the brand of football that the club have played over the last couple of years is something that interests me and the type of player I am.
“Once I knew the interest I always wanted to come here.
“It is a club that’s on the up and I am delighted to be here.”
Thistle manager Alan Archibald has also signed 19-year-old goalkeeper Jamie Sneddon on a two-year deal from Cowdenbeath
Archibald told the club’s official website: “Blair is a player who we have been monitoring for a while and I am delighted to see him sign for us today.
‘’He is an exciting young player who will add a really strong threat to our wide areas.
‘’I think Blair will bring a creative force to our team and I hope he can continue the excellent form he showed at the end of last season. We have a really good group of lads and I definitely think Spittal complements what is already here.’’