Lawless, riding in the blue leaders jersey, finished the final day behind stage winner Greg van Avermaet to secure a win for Team Ineos on home turf.
Ineos rider, Eddie Dunbar, came in third on the stage, managing to seal third in the overall too.
Team Ineos was only officially launched last week, replacing Team Sky.
After the win, Chris Lawless said:
"I can't believe it,"
"If someone had told me I'd win this race before it started I'd have called them a liar.
"I started losing touch halfway up the Otley Chevin but I knew if I could get back on there was a climb around 5km from the finish that I could get over.
"I knew I could follow Greg van Avermaet when he went. Greg was someone I looked up to when I first started riding so to beat him [in the general classification] is special.
"I've got to thank the team for backing me because I don't have a good history on stages like this but they said they'd give me a chance."
When asked how big a win it is for him personally, he replied:
After 150km of racing through the Yorkshire Dales, the final stage exploded on the final categorised climb of the race - the Cote de Otley Chevin - with about 20km remaining.
Four-time Tour de France champion Froome, went on the attack and his effort forced other teams pursuing the overall victory to try to chase him down.
Ineos teammate Eddie Dunbar had also followed the attack. Leapfrogging Froome, he then launched a secondary move as the riders crested the hill and quickly broke clear, chasing down and passing three French riders who were part of the day's original break.
Realising that Dunbar could go on and win the overall title, Froome disrupted the pace of the chasing pack and that, in turn, gave Lawless the chance to catch up.
Eventually, defending champion Van Avermaet, who started the day six seconds behind Lawless, had to attack and while he quickly caught Dunbar, Lawless went with him. That left the Belgian CCC rider with two Ineos riders for company and with an almost impossible task of shaking them both off.
Knowing his fate was sealed, Van Avermaet took the stage win, with Lawless happy to follow him over the line and secure the title by two seconds.
Stage four result:
1. Greg van Avermaet (Bel/CCC Team) 4hrs 40mins 03secs
2. Christopher Lawless (GB/Team Ineos) same time
3. Edward Dunbar (Ire/Team Ineos) +02secs
4. Tom-Jelte Slagter (Ned/Dimension Data) +09secs
5. James Shaw (GB/Swiftcarbon Pro Cycling) Same time
6. Matthew Holmes (GB/Madison Genesis)
7. Alexander Kamp (Den/Riwal Readynez)
8. Gabriel Cullaigh (GB/Team Wiggins Le Col) +12secs
9. Jenthe Biermans (Bel/Katusha Alpecin)
10. Scott Thwaites (GB/Vitus Pro Cycling)
1. Christopher Lawless (GB/Team Ineos) 15hrs 18mins 12secs
2. Greg Van Avermaet (Bel/CCC Team) +02secs
3. Edward Dunbar (Ire/Team Ineos) +11secs
4. Alexander Kamp (Ned/Riwal Readynez) +15secs
5. James Shaw (GB/Swiftcarbon Pro Cycling) +25secs
6. Matthew Holmes (GB/Madison Genesis) Same time
7. Tom-Jelte Slagter (Ned/Dimension Data)
8. Scott Thwaites (GB/Vitus Pro Cycling) +28secs
9. Connor Swift (GB/Madison Genesis) same time
10. Nick van der Lijke (Ned/Roompot-Charles)
Credits/Resources: BBC / Ineos